Step 1) Solve the second equation for y:
y + 4x = 16
y + 4x - color(red)(4x) = 16 - color(red)(4x)
y + 0 = 16 - 4x
y = 16 - 4x
Step 2) Substitute (16 - 4x) for y in the first equation and solve for x:
7y - 6x - 5 = 0 becomes:
7(16 - 4x) - 6x - 5 = 0
(7 * 16) - (7 * 4x) - 6x - 5 = 0
112 - 28x - 6x - 5 = 0
112 - 5 - 28x - 6x = 0
(112 - 5) + (-28 - 6)x = 0
107 + (-34)x = 0
107 + (-34)x + color(red)(34x) = 0 + color(red)(34x)
107 + 0 = 34x
107 = 34x
107/color(red)(34) = (34x)/color(red)(34)
107/34 = (color(red)(cancel(color(black)(34)))x)/cancel(color(red)(34))
107/34 = x
x = 107/34
Step 3) Substitute 107/34 for x in the solution to the second equation at the end of Step 1 and calculate y:
y = 16 - 4x becomes:
y = 16 - (4 xx 107/34)
y = (34/34 xx 16) - 428/34
y = 544/34 - 428/34
y = 116/34
y = (2 xx 58)/(2 xx 17)
y = (color(red)(cancel(color(black)(2))) xx 58)/(color(red)(cancel(color(black)(2))) xx 17)
y = 58/17
The solution is: x = 107/34 and y = 58/17 or (107/34, 58/17)
