Step 1) Solve the second equation for yy:
6x + 2y = -46x+2y=−4
-color(red)(6x) + 6x + 2y = -color(red)(6x) - 4−6x+6x+2y=−6x−4
0 + 2y = -6x - 40+2y=−6x−4
2y = -6x - 42y=−6x−4
(2y)/color(red)(2) = (-6x - 4)/color(red)(2)2y2=−6x−42
(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = (-6x)/color(red)(2) - 4/color(red)(2)
y = -3x - 2
Step 2) Substitute (-3x - 2) for y in the first equation and solve for x:
5x + 8y = -2 becomes:
5x + 8(-3x - 2) = -2
5x + (8 * -3x) - (8 * 2) = -2
5x - 24x - 16 = -2
(5 - 24)x - 16 = -2
-19x - 16 = -2
-19x - 16 + color(red)(16) = -2 + color(red)(16)
-19x - 0 = 14
-19x = 14
(-19x)/color(red)(-19) = 14/color(red)(-19)
(color(red)(cancel(color(black)(-19)))x)/cancel(color(red)(-19)) = -14/19
x = -14/19
Step 3) Substitute -14/19 for x in the solution to the second equation at the end of Step 1 and calculate y:
y = -3x - 2 becomes:
y = (-3 xx -14/19) - 2
y = 42/19 - 2
y = 42/19 - (19/19 * 2)
y = 42/19 - 38/19
y = 4/19
The Solution Is: x = -14/19 and y = 4/19 or (-14/19, 4/19)
