Use the linear combination method to solve this system of equations. What is the value of x? 3x+7y=31 and - 3x-2y=-1

Solve the following system:

{3 x + 7 y = 31 | (equation 1)

-3 x - 2 y = - 1 | (equation 2)

Add equation 1 to equation 2:

{3 x + 7 y = 31 | (equation 1)

0 x+5 y = 30 | (equation 2)

Divide equation 2 by 5:

{3 x + 7 y = 31 | (equation 1)

0 x+y = 6 | (equation 2)

Subtract 7 * (equation 2) from equation 1:

{3 x+0 y = - 11 | (equation 1)

0 x+y = 6 | (equation 2)

Divide equation 1 by 3:

{x+0 y = (-11) / 3 | (equation 1)

0 x+y = 6 | (equation 2)

Collect results:

Answer: x = - 11/3, y = 6

in this one, is about the same as the previous one, if you set them both at y = mx+b, slope-intercept form, you'll notice the slopes are the same, whilst the y-intercepts differ.

so both lines are parallel, and never meet.