Question

Solve the system by substitution.
5, x, minus, 4, y, equals, 1
5x−4y=
1
x, equals, 7, y, minus, 6
x=
7y−6

Answer 1

We have the system
5x − 4y = 1
x = 7y − 6

Substitute x = 7y − 6 into the first equation:
5(7y − 6) − 4y = 1
35y − 30 − 4y = 1
31y − 30 = 1
31y = 31
y = 1

Then x = 7(1) − 6 = 1.

Solution: (x, y) = (1, 1). (Check: 5(1) − 4(1) = 1.)