Name ________________________________________ Date __________________ Class__________________
LESSON
3-2
Reteach
Using Algebraic Methods to Solve Linear Systems
To use the substitution method to solve a system of linear equations:
1. Solve one equation for one variable.
2. Substitute this expression into the other equation.
3. Solve for the other variable.
4. Substitute the value of the known variable in the equation in Step 1.
5. Solve for the other variable.
Use this equation.
6. Check the values in both equations.
It is solved for y.
⎧y = x + 2
⎨
⎩2 x + y = 17
Use the substitution
method when the
coefficient of one of the
variables is 1 or −1.
2 x + y = 17
2x + (x + 2) = 17
Substitute x + 2 for y.
3x + 2 = 17
Simplify and solve for x.
3x = 15
x=5
Substitute x = 5 into y = x + 2 and solve for y: y = x + 2
y=5+2
y=7
The solution of the system is the ordered pair (5, 7).
Check using both equations:
y = x + 2;
7 =? ( 5 ) + 2 ;
2x + y = 17;
2 ( 5 ) + 7 =? 17 ;
7 = 79
17 = 179
Use substitution to solve each system of equations.
⎧y = 2x − 5
1. ⎨
⎩3 x + y = 10
⎧3 x + 2y = 1
2. ⎨
⎩x − y = 2
Use y = 2x − 5.
Solve for x: x − y = 2.
3x + ________ = 10
x = ______________
____________________
3(__________) + 2y = 1
_________________________________________
________________________________________
_________________________________________
________________________________________
Ordered pair solution: ______________
Ordered pair solution: ____________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
3-14
Holt Algebra 2
Name ________________________________________ Date __________________ Class__________________
LESSON
3-2
Reteach
Using Algebraic Methods to Solve Linear Systems (continued)
To use the elimination method to solve a system of linear equations:
1. Add or subtract the equations to eliminate one variable.
2. Solve the resulting equation for the other variable.
3. Substitute the value for the known variable into one of the original equations.
4. Solve for the other variable.
5. Check the values in both equations.
The y terms have
⎧3 x + 2y = 7
opposite coefficients,
⎨
⎩5 x − 2y = 1
Use the elimination
so add.
method when the
3 x + 2y = 7
coefficients of one of
Add the equations.
+ 5 x − 2y = 1
the variables are the
same or opposite.
8x = 8
Solve for x.
x=1
Substitute x = 1 into 3x + 2y = 7 and solve for y: 3x + 2y = 7
3(1) + 2y = 7
2y = 4
y=2
The solution to the system is the ordered pair (1, 2).
Check using both equations:
3 x + 2y = 7
5x − 2y = 1
3 (1) + 2 ( 2 ) =? 7
5 (1) − 2 ( 2 ) =? 1
7 = 79
1 = 19
Use elimination to solve each system of equations.
⎧2 x + y = 1
3. ⎨
⎩−2 x − 3 y = 5
⎧3 x + 4 y = 13
4. ⎨
⎩5 x − 4 y = −21
2x + y = 1
+ (−2x − 3y = 5)
3x + 4y = 13
+ 5x − 4y = −21
−2y = _____
_____________
y = _____
x = ________
________________________________
Ordered pair solution: _______________
Ordered pair solution: _______________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
3-15
Holt Algebra 2
11. a. 102
LESSON 3-3
b. 96
Practice A
Reteach
1.
1. 2x − 5; 5x − 5 = 10; x = 3; y = 2(3) − 5 = 1;
(3, 1)
2. y + 2; y + 2; y = −1; x = −1 + 2 = 1; (1, −1)
3. 6; −3; x = 2; (2, −3)
4. 8x = − 8; −1; y = 4; (−1, 4)
Challenge
1. y = −3x + 22
2. y = x + 6
3. y = 3x − 14
4. y = −2.5x + 3.5
5. y = −8x
6. y = x2 − 2x + 1
Possible answer: The solution region is
the area where the two shading patterns
overlap.
7. y = x2 − 4x + 8
2.
Problem Solving
⎧0.18 x + 0.10 y = ( 0.15 ) 50
1. a. ⎨
⎩ x + y = 50
b. 31.25 lb of Feed X and 18.75 lb of
Feed Y
⎧0.18 x + ( 0.10 ) (15 ) = ( 0.12 ) z
2. a. ⎨
⎩ x + 15 = z
b. 5 lb of Feed X
3.
c. 20 lb of the mixture
3. A
4. B
5. D
6. C
Reading Strategies
1. Possible answer: substitution because I
can easily solve the first equation for y
2. Possible answer: elimination because I
can eliminate x from the system by
adding the two equations together
4.
3. Possible answer: substitution because I
can easily solve the second equation for x
4. Possible answer: elimination because I
can eliminate y from the system by
multiplying the second equation by 2,
then adding the equations
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A31
Holt Algebra 2