Equations and inequalities Equations and inequalities Topic 3: Two-step equations QUESTION 1 a d g Solve the following two-step equations. 2x + 7 = 17 _______________ c 9y – 4 = 23 _____________ ________________________ ________________________ _______________________ 6a – 5 = 25 _______________ e 8a + 7 = 47 _______________ f 3m 5 = 6 _______________ ________________________ ________________________ _______________________ 3x – 1 = 5 _______________ x–3 5 = 4 _______________ QUESTION 2 b h 3x + 8 = 32 ______________ a 3 – 2 = 9 _______________ 5x – 5 = 30 ______________ b a e h 2y + 5 = 35 ______________ 5t – 2 = 8 ______________ 3y + 2 = 5 ______________ x–3 4 = 6 ______________ ________________________ 50 4a – 2·5 = 9·5 ____________ x 2 + 7 = 12 ______________ 7p – 8 = 13 ____________ _______________________ f 6a + 112 = 412 ____________ _______________________ i x–3 2 = 8 _______________ _______________________ Solve these equations. b 7y – 3 = 4 ______________ c ________________________ e m–3 4 = 5 ______________ h 5y – 4 = 26 _____________ f 2y + 8 = –2 ______________ 2x – 1 = 17 _____________ _______________________ i ________________________ k 8x – 6 = 26 ______________ _______________________ ________________________ ________________________ j c ________________________ ________________________ g 8y – 3 = 21______________ ________________________ ________________________ d 3x – 2 = 19 _____________ _______________________ ________________________ ________________________ QUESTION 3 i Solve the following equations. ________________________ g a 2 – 4 = 6 _______________ ________________________ ________________________ d page 151 UNIT 3: Two-step equations ________________________ a ANSWERS 2x – 5 = 11 ____________ _______________________ l ________________________ 4p – 6 = –10 ____________ _______________________ EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 1 Equations and Inequalities Mathletics Instant Workbooks – Series K Copyright © 3P Learning 3 Simultaneous Simultaneousequations equations ANSWERS page 161 UNIT 2: The substitution method Topic 2: The substitution method QUESTION 1 Solve the following pairs of simultaneous equations by substitution. a c e b x+y=6 x–y=4 2x + 3y = 6 x – 3y = 12 _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ x – 4y = 16 –x + 8y = 12 d x + 5y = 8 2x – 5y = 4 _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ 3m + 4n = 12 m + 4n = 4 f 2p + 5q = 7 p – 4q = 36 _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ QUESTION 2 Use the method of substitution to solve the following pairs of simultaneous equations. a c 114 b 2x + y = 7 3x – 2y = 14 x + 3y = 9 x – 3y = 3 _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ 4x – 5y = 14 x + 2y = 23 d x + 2y = 8 3x – y = 24 _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 1 Simultaneous equations Mathletics Instant Workbooks – Series K Copyright © 3P Learning 2 Simultaneous equations Simultaneous equations ANSWERS page 161 UNIT 4: The elimination method Topic 4: The elimination method QUESTION 1 Solve the following pairs of simultaneous equations by the method of elimination. a c e x + 3y = 4 x – 3y = 10 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 2a + 5b = 8 3a – 5b = 7 _______________________________________ _______________________________________ _______________________________________ _______________________________________ a+b=7 a–b=9 _______________________________________ _______________________________________ _______________________________________ _______________________________________ b d f 5x – 2y = 11 3x + 2y = 5 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 3x – y = 5 8x + y = 6 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 4x + 7y = 14 3x – 7y = 7 _______________________________________ _______________________________________ _______________________________________ _______________________________________ QUESTION 2 Use the method of elimination to solve the following pairs of simultaneous equations. a c e 116 x + 3y = 12 x – 5y = 4 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 2a + 5b = 16 2a – 3b = –8 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 3x + 8y = 12 3x – 2y = 2 _______________________________________ _______________________________________ _______________________________________ _______________________________________ b d f 12m + 5n = 45 3m + 5n = 9 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 5x + 2y = 15 3x + 2y = 9 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 4m + 9n = 15 2m + 9n = 7 _______________________________________ _______________________________________ _______________________________________ _______________________________________ EXCEL ESSENTIAL SKILLS: YEAR 1- MATHEMATICS REVISION AND EXAM WORKBOOK 1 Simultaneous equations Mathletics Instant Workbooks – Series K Copyright © 3P Learning 4 Simultaneous equations Simultaneous equations ANSWERS page 161 UNIT 5: Elimination method involving different coefficients Topic 5: Elimination method involving different coefficients QUESTION 1 Solve the following pairs of simultaneous equations by the method of elimination. a c e 2x + 3y = 6 x–y=3 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 3a + 5b = 6 2a + b = 4 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 5x – 2y = 7 3x + y = 2 _______________________________________ _______________________________________ _______________________________________ _______________________________________ b d f 4x + 7y = 8 x–y=2 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 4m – 5n = –14 2m + 3n = 4 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 2a – 5b = 3 5a – 2b = –3 _______________________________________ _______________________________________ _______________________________________ _______________________________________ QUESTION 2 Use the method of elimination to solve the following pairs of simultaneous equations. a c e 3x + y = 5 x + 3y = 7 _______________________________________ _______________________________________ _______________________________________ _______________________________________ x + 3y = 18 2x – 4y = 6 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 2x + 3y = 1 4x – y = 9 _______________________________________ _______________________________________ _______________________________________ _______________________________________ b d f 2m + n = 6 3m – 2n = 2 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 4x + 9y = 4 3x – y = 3 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 5x + 2y = 2 –x + 3y = 3 _______________________________________ _______________________________________ _______________________________________ _______________________________________ 117 Chapter 10: Simultaneous equations Simultaneous equations Mathletics Instant Workbooks – Series K Copyright © 3P Learning 5 Simultaneous Simultaneousequations equations ANSWERS page 162 UNIT 6: Using simultaneous equations to solve worded problems Topic 6: Using simultaneous equations to solve worded problems QUESTION 1 a The sum of two numbers is 35 and their difference is 19. Find the numbers. ________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ b The sum of two numbers is 72. Twice the first number minus the second number is equal to 54. Find the numbers. ______________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ There are 840 students in a school. If there are 120 more girls than boys, how many boys and girls are there? ________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ The difference between the length and width of a rectangular room is 8 m and the perimeter of the room is 64 m. Find the length and width of the room. _______________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ c d QUESTION 2 a Four apples and five oranges cost $3.20 whereas two apples and three oranges cost $1.80. Find the price of each piece of fruit. ________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ b Maddie is four years older than her brother Angus. If the sum of their ages is 30 years, what are their ages? _________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ Suzie is four times as old as her daughter Samantha. The sum of their ages is 70 years. Find their ages. ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ c 118 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 1 Simultaneous equations Mathletics Instant Workbooks – Series K Copyright © 3P Learning 6
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