Question

Solve the system of equations using the substitution method.

{y=−3x+7
x=−2y−16



Enter your answers in the boxes.

x=



y=

Answer 1

x = 6 and y = -11

Explanation:

Given : System of linear equation

y=−3x+7

x=−2y−16

We have to solve the system of equations using the substitution method.

In substitution method, we substitute the value of one variable in term of other and solve for it.

Consider the given system of linear equation

y = −3x + 7 ...(1)

x = −2y − 16 .....(2)

Substitute, (2) in (1), we get,

y = -3(-2y - 16) + 7

Simplify , we get,

y = 6y + 48 + 7

6y - y = - 55

5y = -55

y = -11

Substitute y = -11 in (2), we get,

x = −2(-11) − 16 = 22 - 16 = 6

thus, x = 6

Thus , x = 6 and y = -11

Answer 2

`x = 6`

`y = - 11`

EXPLANATION

The given system of equations is

`y = - 3x + 7...(1)`

and

`x = - 2y - 16...(2)`

We substitute equation (1) into equation (2) to get;

`x = - 2( - 3x + 7) - 16`

`x = 6x - 14- 16`

We group similar terms

`x - 6x = - 14 - 16`

`- 5x = - 30`

Divide both sides by -5.

`x =6`

Put x=6 into equation (1).

`y = - 3(6) + 7`

`y = - 18 + 7`

`y = - 11`