Step 1) Solve the first equation for y:
5x + y = -7
-color(red)(5x) + 5x + y = -color(red)(5x) - 7
0 + y = -5x - 7
y = -5x - 7
Step 2) Substitute (-5x - 7) for y in the second equation and solve for x:
6x + 7y = -9 becomes:
6x + 7(-5x - 7) = -9
6x + (7 * -5x) - (7 * 7) = -9
6x + (-35x) - 49 = -9
6x - 35x - 49 = -9
(6 - 35)x - 49 = -9
-29x - 49 = -9
-29x - 49 + color(red)(49) = -9 + color(red)(49)
-29x - 0 = 40
-29x = 40
(-29x)/color(red)(-29) = 40/color(red)(-29)
(color(red)(cancel(color(black)(-29)))x)/cancel(color(red)(-29)) = -40/29
x = -40/29
Step 3) Substitute -40/29 for x in the solution to the first equation at the end of Step 1 and calculate y:
y = -5x - 7 becomes:
y = (-5 xx -40/29) - 7
y = 200/29 - 7
y = 200/29 - (29/29 xx 7)
y = 200/29 - 203/29
y = -3/29
The solution is: x = -40/29 and y = -3/29 or (-40/29, -3/29)
