1. Solving Systems of Equations Test Corrections

2. Solve each system of equations by graphing.
1. y = -3x – y = 3x – 4
y = 3x y = 2x – 2
(-1, -1)
(0, -2)

3. Solve each system of equations by substitution.
3. y = -x – 2
6x + 2y = 0
6x + 2(-x – 2) = 0  Substitute 1st equation
6x – 2x – 4 = 0  Distribute
4x = 4  Add 4 to both sides
x = 1  Divide both sides by 4
y = -x – 2
y = -(1) – 2
y = -3
(1, -3)

4. Solve each system of equations by substitution.
4. y = 4x – 4
y = x + 5
4x – 4 = x  Set equations equal to each other
-x x  Subtract x from both sides
3x – 4 = 5  Simplify
 Add 4 to both sides
3x = 9  Simplify
x = 3  Divide both sides by 3
y = x + 5
y = (3) + 5
y = 8
(3, 8)

5. Solve each system of equations by elimination.
5. 2x + y = 4  Multiply by 2  4x + 2y = 8
6x – 2y = –8
4x + 2y = 8
+ 6x – 2y = -8
8x = 0
x = 0
2x + y = 4
2(0) + y = 4
y = 4
(0, 4)

6. Solve each system of equations by elimination.
6. 4x – y = 1
+ 2x + y = 11
6x = 12
x = 2
2x + y = 11
2(2) + y = 11
4 + y = 11
y = 7
(2, 7)

7. Tell how many solutions each system of equations has.
3x – 2y = 2
3x – 2y = 0
No Solution
Slopes are the same and y-intercepts are different; will have parallel lines
8. 2x + y = 5
4x + 2y = 10
Infinitely Many Solutions
The lines are the same – multiply the 1st equation by 2

8. 9. The Lopez family bought 2 adult tickets and 3 child’s tickets to the carnival. They spent a total of $23. The James family bought 4 adult tickets and 2 child’s tickets to the carnival. They spent a total of $34. How much did each type of ticket cost?
a = cost of 1 adult ticket
c = cost of 1 child ticket
2a + 3c = 23
4a + 2c = 34
Multiply 1st equation by -2, then add
-4a – 6c = -46
+ 4a + 2c = 34
-4c = -12
c = 3
Child ticket = $3
2a + 3c = 23
2a + 3(3) = 23
2a + 9 = 23
2a = 14
a = 7
Adult ticket = $7

9. 10. Theo sells bird feeders for $8 each and birdhouses for $12 each
10. Theo sells bird feeders for $8 each and birdhouses for $12 each. At a craft fair, he sold 25 items for a total of $240. How many birdhouses did he sell?
f = number of bird feeders h = number of birdhouses f + h = 25 8f + 12h = 240 Multiply 1st equation by -8, then add
-8f – 8h = -200
+ 8f + 12h = 240
4h = 40
h = 10
Theo sold 10 birdhouses.