Step 1) Solve the second equation for y:
-13x + y = 8
color(red)(13x) - 13x + y = color(red)(13x) + 8
0 + y = 13x + 8
y = 13x + 8
Step 2) Substitute (13x + 8) for y in the first equation and solve for x:
5x - 7y = -43 becomes:
5x - 7(13x + 8) = -43
5x - (7 * 13x) - (7 * 8) = -43
5x - 91x - 56 = -43
(5 - 91)x - 56 = -43
-86x - 56 = -43
-86x - 56 + color(red)(56) = -43 + color(red)(56)
-86x - 0 = 13
-86x = 13
(-86x)/color(red)(-86) = 13/color(red)(-86)
(color(red)(cancel(color(black)(-86)))x)/cancel(color(red)(-86)) = -13/86
x = -13/86
Step 3) Substitute -13/86 for x in the solution to the second equation at the end of Step 1 and calculate y;
y = 13x + 8 becomes:
y = (13 * -13/86) + 8
y = -169/86 + 8
y = -169/86 + (86/86 xx 8)
y = -169/86 + 688/86
y = 519/86
The solution is: x = -13/86 and y = 519/86 or (-13/86, 519/86)
