Question

A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 3.
Review the graphs of a system of two linear equations in two variables: x−5y=7
and 3x−2y=−4
. Find the solution to both equations.

(1 point)
The intersection point is (
).

Answer 1

Solve by substitution: 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.

The intersection point is (−34/13, −25/13).