Step 1) Solve the first equation for x:
x + 3y = 8
x + 3y - color(red)(3y) = 8 - color(red)(3y)
x + 0 = 8 - 3y
x = 8 - 3y
Step 2) Substitute 8 - 3y for x in the second equation and solve for y:
-x + 9y = 16 becomes:
-(8 - 3y) + 9y = 16
-8 + 3y + 9y = 16
-8 + (3 + 9)y = 16
-8 + 12y = 16
color(red)(8) - 8 + 12y = color(red)(8) + 16
0 + 12y = 24
12y = 24
(12y)/color(red)(12) = 24/color(red)(12)
(color(red)(cancel(color(black)(12)))y)/cancel(color(red)(12)) = 2
y = 2
Step 3) Substitute 2 for y into the solution for the first equation at the end of Step 1 and calculate x:
x = 8 - 3y becomes:
x = 8 - (3 * 2)
x = 8 - 6
x = 2
The solution is: x = 2 and y = 2 or (2, 2)