Question

I am doing solving systems of equations and my problems are x=7-2y and y=8x+2

Answer 1

Answer: x =
`(3)/(17)`, y =
`(58)/(17)`

Explanation:

We will solve the given system of equations by substitution.

Given:

x = 7 - 2y

Substitute:

x = 7 - 2(8x+2)

Distribute:

x = 7 - 16x - 4

Simplify:

x = 3 - 16x

Add 16x to both sides of the equation:

17x = 3

Divide both sides of the equation by 3:

x =
`(3)/(17)`

Next, we will do the same to solve for y. We can also substitute the value of x we found above, but I will show solving by substitution for both variables here.

Given:

y = 8x + 2

Substitute:

y = 8(7-2y) + 2

Distribute:

y = 56 - 16y + 2

Simplify:

y = 58 - 16y

Add 16y to both sides of the equation:

17y = 58

Divide both sides of the equation by 17:

y =
`(58)/(17)`