Step 1) Solve the second equation for yy:
4x + y - color(red)(4x) = 10 - color(red)(4x)4x+y−4x=10−4x
4x - color(red)(4x) + y = 10 - color(red)(4x)4x−4x+y=10−4x
0 + y = 10 - 4x0+y=10−4x
y = 10 - 4xy=10−4x
Step 2) Substitute color(red)(10 - 4x)10−4x for yy in the first equation and solve for xx:
3x + 5(10 - 4x) = 53x+5(10−4x)=5
3x + 50 - 20x = 53x+50−20x=5
3x - 20x + 50 = 53x−20x+50=5
-17x + 50 = 5−17x+50=5
-17x + 50 + color(red)(17x) - color(blue)(5) = 5 + color(red)(17x) - color(blue)(5)−17x+50+17x−5=5+17x−5
-17x + color(red)(17x) + 50 - color(blue)(5) = 5 - color(blue)(5) + color(red)(17x)−17x+17x+50−5=5−5+17x
0 + 50 - 5 = 0 + 17x0+50−5=0+17x
45 = 17x45=17x
45/color(red)(17) = (17x)/color(red)(17)4517=17x17
45/17 = (color(red)(cancel(color(black)(17)))x)/cancel(color(red)(17))
45/17 = x
x = 45/17
Step 3) Substitute color(red)(45/17) for x in the solution to the second equation at the end of Step 1:
y = 10 - (4 xx 45/17)
y = (17/17 xx 10) - (180/17)
y = 170/17 - 180/17
y = -10/17
The solution is: x = 45/17, y = -10/17 or (45/17, -10/17)
