Question

Review the graphs of a system of two linear equations in two variables: x−5y=7
𝑥
−
5
𝑦
=
7
and 3x−2y=−4
3
𝑥
−
2
𝑦
=
−
4
. Find the solution to both equations.

Answer 1

Solve by substitution. From x − 5y = 7, x = 7 + 5y. Substitute into 3x − 2y = −4:

3(7 + 5y) − 2y = −4
21 + 15y − 2y = −4
13y = −25
y = −25/13.

Then x = 7 + 5(−25/13) = 91/13 − 125/13 = −34/13.

Solution: (x, y) = (−34/13, −25/13).