Step 1) Solve the first equation for xx:
x + 8y = 3x+8y=3
x + 8y - color(red)(8y) = 3 - color(red)(8y)x+8y−8y=3−8y
x + 0 = 3 - 8yx+0=3−8y
x = 3 - 8yx=3−8y
Step 2) Subsitute 3 - 8y3−8y for xx in the second equation and solve for yy:
4x + 5y = -24x+5y=−2 becomes:
4(3 - 8y) + 5y = -24(3−8y)+5y=−2
(4 * 3) - (4 * 8y) + 5y = -2(4⋅3)−(4⋅8y)+5y=−2
12 - 32y + 5y = -212−32y+5y=−2
12 + (-32 + 5)y = -212+(−32+5)y=−2
12 - 27y = -212−27y=−2
-color(red)(12) + 12 - 27y = -color(red)(12) - 2−12+12−27y=−12−2
0 - 27y = -140−27y=−14
-27y = -14−27y=−14
(-27y)/color(red)(-27) = (-14)/color(red)(-27)−27y−27=−14−27
(color(red)(cancel(color(black)(-27)))y)/cancel(color(red)(-27)) = 14/27
y = 14/27
Step 3) Substitute 14/27 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = 3 - 8y becomes:
x = 3 - (8 * 14/27)
x = 3 - 112/27
x = (3 * 27/27) - 112/27
x = 81/27 - 112/27
x = -31/27
The solution is: x = -31/27 and y = 14/27 or (-31/27, 14/27)
