Check Worksheet 3
• On Socrative:
• Put in your answers to the selected questions.
• Room Name: mrcosgrove
Questions 25 – 28
• *Solve like a normal equation.
• Example:
|x| + 3 = 10
•
|x| = 10 – 3
•
|x| = 7
•
So x can be either +7 or - 7
Important Dates
• Diagnostic Test (not included on PowerSchool)
• Tuesday September 2nd
• Quiz on Review Sheets 1-4
• Thursday September 3rd
Simultaneous Equations
LO: To be able to solve Simultaneous Equations by
adding or subtracting. Also called ‘Systems of Linear
Equations’
STARTER: Expand & Simplify:
1) 3(x + 4) + 4(x + 7)
2) 2(3y + 6) + 3(2y – 4)
3) 6(2m – 10) – 4(5m + 3)
1) 7x + 30
2) 12y
3) -8m -72
Why do we need to use Simultaneous Equations?
=80p
= 50p
= 30p
=£1.30
Why do we need to use Simultaneous Equations?
When we have 2 different unknown letters, we can solve the
equations at the same time (simultaneously).
Bronze:
Solve: 6x + y = 15
4x + y = 11
Silver:
Solve: 4x + 3y = 27
2x + y = 17
Gold:
Solve: 2x + 3y = 30
5x + 7y = 71
Solving Simultaneous Equations – Example 1
Bronze:
We have 2 unknowns: x and y
Solve: 6x + 1y = 15 (1)
4x + 1y = 11 (2)
Step 1: Eliminate the letter
with the same co-efficient
(by SUBTRACTING in this
question)…
6x + 1y = 15
4x + 1y = 11 2x
= 4
x=2
SAME SIGN
SUBTRACT
Step 2: To find y, we substitute
x = 2 back into one of the original
equations (equation 1)
(6 x 2) + y = 15
12 + y = 15
(-12)
y=3
Solving Simultaneous Equations – Example 1
Bronze:
We have 2 unknowns: x and y
Solve: 6x + 1y = 15 (1)
4x + 1y = 11 (2)
SAME SIGN
SUBTRACT
Step 3: Check your answers using equation (2)…
x= 2, y = 3
(4 x 2) + 3 = 11
8 + 3 = 11
11 = 11
When Co-Efficient’s are not the same…
Silver:
SAME SIGN
SUBTRACT
Solve: 3x + 3y = 18 (1)
5x + y = -2 (2)
Step 1: When neither co-efficient’s are
the same we multiply one or both
equations to make them the same…
Step 2: Eliminate the letter with
the same co-efficient (by
SUBTRACTING in this question)
Multiply equation (2) by x3
15x + 3y = -6 (3)
(3) 15x + 3y = -6
(1) 3x + 3y = 18 –
12x
We call this equation (3)
We use the original equation 1
and new equation 3.
= - 24
(÷ 12)
x = -2
When Co-Efficient’s are not the same…
Silver:
Solve: 3x + 3y = 18 (1)
5x + y = -2 (2)
Step 3: To find y, we substitute
x = -2 back into one of the
original equations (equation 1)
(3 x -2) + 3y = 18
-6 + 3y = 18
(+ 6)
3y = 24
(÷ 3)
y=8
Step 4: Check your answers
using equation 2
x = -2, y = 8
(5 x -2) + 8 = -2
-10 + 8 = -2
-2 = -2
When Co-Efficient’s are not the same… (A Grade)
Gold:
Solve: 2x + 3y = 30 (1)
5x + 7y = 71 (2)
Step 1: When neither co-efficient’s
are the same we may need to
multiply both equations to make
them the same…
SAME SIGN
SUBTRACT
Step 2: Eliminate the letter with
the same co-efficient (by
SUBTRACTING in this question)
Multiply equation (1) by x7
14x + 21y = 210 (3)
We call this equation (3)
Multiply equation (2) by x3
15x + 21y = 213 (4)
We call this equation (4)
Now we solve using equation (3) & (4)
(4) 15x + 21y = 213
(3) 14x + 21y = 210 –
x
= 3
So x = 3
When Co-Efficient’s are not the same… (A Grade)
Gold:
Solve: 2x + 3y = 30 (1)
5x + 7y = 71 (2)
Step 3: To find y, we substitute
x = 3 back into one of the
original equations (equation 1)
(2 x 3) + 3y = 30
6 + 3y = 30
(- 6)
3y = 24
(÷ 3)
y=8
Step 4: Check your answers
using equation 2
x = 3, y = 8
(5 x 3) + (7 x 8) = 71
15 + 56 = 71
71 = 71
Plenary
The sum of two numbers is 19 and their
difference is 5. Find the value of each of the
numbers.
Review Sheet 4
• Questions 1-5
• Question 6 as extension