Step 1) Solve the second equation for xx:
x - 3y = 1x−3y=1
x - 3y + color(red)(3y) = 1 + color(red)(3y)x−3y+3y=1+3y
x - 0 = 1 + 3yx−0=1+3y
x = 1 + 3yx=1+3y
Step 2) Substitute 1 + 3y1+3y for xx in the first equation and solve for yy:
8x + 3y = -98x+3y=−9 becomes:
8(1 + 3y) + 3y = -98(1+3y)+3y=−9
(8 * 1) + (8 * 3y) + 3y = -9(8⋅1)+(8⋅3y)+3y=−9
8 + 24y + 3y = -98+24y+3y=−9
8 + 27y = -98+27y=−9
-color(red)(8) + 8 + 27y = -color(red)(8) - 9−8+8+27y=−8−9
0 + 27y = -170+27y=−17
27y = -1727y=−17
(27y)/color(red)(27) = -17/color(red)(27)27y27=−1727
(color(red)(cancel(color(black)(27)))y)/cancel(color(red)(27)) = -17/27
y = -17/27
Step 3) Substitute -17/27 for y in the solution to the second equation at the end of Step 1 and calculate x:
x = 1 + 3y becomes:
x = 1 + (3 xx -17/27)
x = 1 - 17/9
x = (9/9 xx 1) - 17/9
x = 9/9 - 17/9
x = -8/9
The solution is: x = -8/9 and y = -17/27 or (-8/9, -17/27)
