Step 1) Solve the first equation for y:
-4x - 2y = 14
color(red)(-1/2)(-4x - 2y) = color(red)(-1/2) xx 14
(color(red)(-1/2) xx -4x) + (color(red)(-1/2) xx -2y) = -7
2x + 1y = -7
2x + y = -7
2x - color(red)(2x) + y = -7 - color(red)(2x)
0 + y = -7 - 2x
y = -7 - 2x
Step 2) Substitute (-7 - 2x) for y in the second equation and solve for x:
-10x + 7y = -2 becomes:
-10x + 7(-7 - 2x) = -2
-10x + (7 xx -7) + (7 xx -2x) = -2
-10x + (-49) + (-14x) = -2
-10x - 49 - 14x = -2
-10x - 14x - 49 = -2
(-10 - 14)x - 49 = -2
-24x - 49 = -2
-24x - 49 + color(red)(49) = -2 + color(red)(49)
-24x - 0 = 47
-24x = 47
(-24x)/color(red)(-24) = 47/color(red)(-24)
(color(red)(cancel(color(black)(-24)))x)/cancel(color(red)(-24)) = -47/24
x = -47/24
Step 3) Substitute -47/24 for x in the solution to the first equation at the end of Step 1:
y = -7 - 2x becomes:
y = -7 - (2 xx -47/24)
y = -7 - (-47/12)
y = -7 + 47/12
y = (12/12 xx -7) + 47/12
y = -84/12 + 47/12
y = -37/12
The Solution Is:
x = -47/24 and y = -37/12
Or
(-47/24, -37/12)
