Step 1) Solve the second equation for y:
4x + y = 10
-color(red)(4x) + 4x + y = -color(red)(4x) + 10
0 + y = -4x + 10
y = -4x + 10
Step 2) Substitute -4x + 10 for y in the first equation and solve for x:
3x - 5y = 53 becomes:
3x - 5(-4x + 10) = 53
3x - (5 * -4x) - (5 * 10) = 53
3x - (-20x) - 50 = 53
3x + 20x - 50 = 53
23x - 50 = 53
23x - 50 + color(red)(50) = 53 + color(red)(50)
23x - 0 = 103
23x = 103
(23x)/color(red)(23) = 103/color(red)(23)
(color(red)(cancel(color(black)(23)))x)/cancel(color(red)(23)) = 103/23
x = 103/23
Step 3) Substitute 103/23 for x in the solution to the second equation at the end of Step 1 and calculate y
y = -4x + 10 becomes:
y = (-4 * 103/23) + 10
y = -412/23 + (10 * 23/23)
y = -412/23 + 230/23
y = -182/23
The solution is: x = 103/23 and y = -182/23
