Question

Using either substitution or elimination method, solve the system of equations that consists of 8x+y= -16 and -3x+y=-5 Your solution will be a coordinate of integers. ​

Answer 1

x= -1

y= -8

Explanation:

Solve for y in 8x + y = -16

y = -16 - 8x

Substitute y = -16 - 8x into -3x + y = -5

-11x - 16 = -5

Solve for x in -11x - 16 = -5

x = -1

Substitute x = -1 into y = -16 - 8x

y = -8

Therefore,

x= -1

y= -8

Answer 2

(-1, -8)

Explanation:

SUBSTITUTION METHOD:

• 8x + y = -16
• -3x + y = -5

Solve for y in the first equation by subtracting 8x from both sides.

• y = -16 - 8x

Substitute this value for y into the second equation.

• -3x + (-16 - 8x) = -5

Remove the parentheses and simplify.

• -3x - 16 - 8x = -5

Combine like terms.

• -11x - 16 = -5

Add 16 both sides of the equation.

• -11x = 11

Divide both sides of the equation by -11.

• x = -1

Substitute this value for x into either equation (I'm using the first equation).

• 8(-1) + y = -16

Multiply and simplify.

• -8 + y = -16

Add 8 to both sides of the equation.

• y = -8

ELIMINATION METHOD:

• 8x + y = -16
• -3x + y = -5

Subtract the second equation from the first equation to "cancel" the y-variable.

• 11x = -11

Divide both sides of the equation by 11.

• x = -1

Substitute this value for x into either equation (I'm using the second equation).

• -3(-1) + y = -5

Multiply and simplify.

• 3 + y = -5

Subtract 3 from both sides of the equation.

• y = -8

The solution to this system of equations is (-1, -8).