Unit 12 Quiz Review System of Equations

Solve the system of equations algebraically. 

x + 2y = 8

2x - y = 1

• (2, 3)

• (3, 2)

• (1, 3)

• (3, 1)

Solve the system of equations algebraically. 

5x + 6y = 3

- 5x - 2y = -11

• (-2, 3)

• (3, -2)

• (1, 3)

• (3, 1)

Look at this system of equations:     

4x -  y = -10

   x + 3y =   -8

Which of the following statements describes the most logical first step in solving this system?

• Multiply the top equation by -4

• Multiply the bottom equation by -4

• Multiply the top equation by -1

• Multiply the bottom equation by -1

    5x + y = 10

      2x + 6y = 20

Which of the following shows the correct factors needed to eliminate the

y variable?

• -6 (5x + y = 10)

  (2x + 6y = 20)

• (5x + y = 10)

  -6 (2x + 6y =20)

• 2 (5x + y = 10)

  (2x + 6y = 20)

• (5x + y = 10)

  5 (2x + 6y = 20)

Is the point (3, 1) a solution to this system?

2x + y = 7

3x - y = 8

Hint: Do a check!

• Yes b/c it's a solution to BOTH equations

• No b/c it's a solution to only the FIRST equation

• No b/c it's a solution to only the SECOND equation

• No, b/c it's not a solution to either equation

If a system of equations has ONE solution, what does it look like graphically?

• Parallel Lines

• Overlapping Lines

• Intersecting Lines

If a system of equations has NO solution, what does it look like graphically?

• Parallel Lines

• Overlapping Lines

• Intersecting Lines

If a system of equations has INFINITE solutions, what does it look like graphically?

• Parallel Lines

• Overlapping Lines

• Intersecting Lines

Solve the system of equations:

y - x = 8

x = 3

• (11, 3)

• (3, 11)

• (8, 11)

• (3, 8)

Solve the system of equations:

y = x + 5

y = -x + 11

• (5, 3)

• (3, 5)

• (8, 3)

• (3, 8)