Substitution: Systems of Equations

Which option correctly substituted the following Systems of Equations?

y = -3x + 19

3x - 2y = -2

• 3(-3x + 19) - 2y = -2

• 3x + 2(-3x + 19) = -2

• 3x - 2(-3x+19) = -2

• 3x - (-3x + 19) = -2

Which of the following is the correct distribution?

3x - 2(-3x + 19) = -2

• 3x - 5x + 17 = -2

• 3x - 6x + 38 = -2

• 3x - 6x - 38 = -2

• 3x + 6x - 38 = -2

Combine Like Terms:

3x + 6x - 38 = -2

• 9x = 36

• 9x = -40

• 3x = 36

• 9x = -36

Solve for x.

9x = 36

• x = 4

• x = 12

• x = 25

• x = -10

We know x = 4 for the following System of Equations:

y = -3x + 19

3x - 2y = -2

Now Solve for y.

• y = -7

• y = 7

• y = -31

• y = 31

Which is the correct substitution?

x = -2y + 4

-5x + 4y = 8

• -5x + 4(-2y + 4) = 8

• -5(-2y - 4) + 4y = 8

• -5(-2y + 4) + 4y = 8

• -2y + 4 + 4y = 8

What is the correct substitution?

y = 2x + 3

y = -3x + 3

• 2x + 3 = -3x + 3

• 2x + 3 = 3x - 3

• y = -3(2x + 3) + 3

• y = 2(-3x + 3) + 3

We know:

2x + 3 = -3x + 3

Solve for x.

• x = -5

• x = 1

• x = 0

• No solution

We know x = 0. Solve for y.

y = 2x + 3

y = -3x + 3

• y = -3

• y= 3

• y = 0

• No Solution

When a System of Equations gets an answer like 5 = 5, which is TRUE, how many solutions does the system have?

• 1 Solution

• No Solution

• Infinite Solutions