Step 1) Solve the second equation for yy:
y + 4x = 16y+4x=16
y + 4x - color(red)(4x) = 16 - color(red)(4x)y+4x−4x=16−4x
y + 0 = 16 - 4xy+0=16−4x
y = 16 - 4xy=16−4x
Step 2) Substitute (16 - 4x)(16−4x) for yy in the first equation and solve for xx:
7y - 6x - 5 = 07y−6x−5=0 becomes:
7(16 - 4x) - 6x - 5 = 07(16−4x)−6x−5=0
(7 * 16) - (7 * 4x) - 6x - 5 = 0(7⋅16)−(7⋅4x)−6x−5=0
112 - 28x - 6x - 5 = 0112−28x−6x−5=0
112 - 5 - 28x - 6x = 0112−5−28x−6x=0
(112 - 5) + (-28 - 6)x = 0(112−5)+(−28−6)x=0
107 + (-34)x = 0107+(−34)x=0
107 + (-34)x + color(red)(34x) = 0 + color(red)(34x)107+(−34)x+34x=0+34x
107 + 0 = 34x107+0=34x
107 = 34x107=34x
107/color(red)(34) = (34x)/color(red)(34)10734=34x34
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)
