6.2 Solving Systems by Substitution

What is y equal to in the first equation in the following system of equations?

y = x - 7

y = 2x - 10

• -7

• -10

• x - 7

• 2x - 10

Which answer option is the correct way to substitute the value for y into the second equation?

y = x - 7

y = 2x - 10

• x - 7 = 2x - 10

• y (x - 7) = 2x - 10

• y = 2 (x - 7)

• x = 2x - 10

Now, solve the equation to find x.

y = x - 7

y = 2x - 10

• x = -1

• x = 1

• x = -3

• x = 3

Now that you have found x to equal 3, substitute that value into either original equation to solve for y.

y = x - 7

y = 2x - 10

• y = 4

• y = -4

• y = 10

• y = 16

What would be the final answer to this system of equations?

y = x - 7

y = 2x - 10

• x = 3 and y = -4

• (-4,3)

• (3,-4)

• (-3,-4)

NEW PROBLEM

What is y equal to in the following system of equations?

3x + 5y = 20

y = -3x - 8

• 3x + 5y

• -3

• 5y = 20

• -3x - 8

Which answer option is the correct way to substitute the value for y into the other equation?

3x + 5y = 20

y = -3x - 8

• 3x + 5(-3x-8)=20

• 3(-3x-8) +5y=20

• -3x-8 = 3x+5y

• 3x + 20 = -3x - 8

Now, solve the equation to find x.

3x + 5y = 20

y = -3x - 8

• x = 4

• x = -5

• x = 5

• x = 20

Now that you have found x to equal -5, substitute that value into either original equation to solve for y.

*HINT: use the equation that starts with y=

3x + 5y = 20

y = -3x - 8

• y = -23

• y = 27

• y = 7

• y = 23

What would be the final answer to this system of equations?

3x + 5y = 20

y = -3x - 8

• (-5,7)

• x = -5 and y=7

• (7,-5)

• (5,-7)