Solving Systems of Equations Test Corrections

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Presentation transcript:

Solving Systems of Equations Test Corrections

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

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)

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

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)

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 -4 -4 y = 7 (2, 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

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

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.