The solution to the following system of linear equations lies in which quadrant? - 2x + 3y = 8 4x + y = - 2

First, let's find the solution.

-2x + 3y = 8

Add 2x to both sides.

3y = 2x + 8

Divide both sides by 3.

y = 2/3x + 8/3

4x + 2/3x + 8/3 = - 2

14/3x + 8/3 = - 2

Subtract 8/3 from both sides.

14/3x = - 14/3

Multiply both sides by 3/14.

x = - 1

y = 2/3 (-1) + 8/3

y = - 2/3 + 8/3

y = 6/3, or 2.

The solution is (-1, 2) which lies in Quadrant II, because its outline is (-, + ).