Answer is (-1/4, -1/2)
x = -1/4, y = -1/2
Step by step.
(A) 2x + 3y + 2 = 0
(B) 2x + y = -1
I like to label my equations first, A and B.
I will change (B) into y intercept form for ease of doing the math.
(A) 2x + 3y + 2 = 0
(B) y = -2x -1
Now we will solve by substituting the y value of B into the y spot in the A equation.
2x + 3(-2x -1) + 2 = 0
Distribute parenthesis first
2x -6x -3 +2 = 0
Combine terms
-4x -1 = 0
Now we want to isolate x on one side of = by adding 1 to both sides
-4x -1 +1 = 0 +1
-4x = 1
Now solve for x
Divide both sides by -4
-4/-4 x = 1/-4
X = -1/4
Now to solve for y, substitute your x value into equation B
y = -2x -1
y = (-2)(-1/4) -1
y = 1/2 -1
y = -1/2
We can check our work by substituting our x and y values into equation B
y = -2x -1
-1/2 = -2(-1/4) -1
-1/2 = 1/2 -1
-1/2 = -1/2
Problem solved!