Question

y = 2 3 x − 5 y = −2x + 3 On a coordinate plane, 2 lines intersect at (negative 3, negative 3). She determined that the solution is (–3, –3). Is she correct? If not, explain why.

Answer 1

Given:

The two equations are:

`y=(2)/(3)x-5`

`y=-2x+3`

To find:

Whether (-3,-3) is a solution of the given equation or not.

Solution:

Table of values for
`y=(2)/(3)x-5`,

x y

0 -5

7.5 0

Plot the points (0,-5) and (7.5,0) on a coordinate plane and connect them by a straight line.

Table of values for
`y=-2x+3`,

x y

0 3

1.5 0

Plot the points (0,3) and (1.5,0) on a coordinate plane and connect them by a straight line.

From the below graph, it is clear that the graphs of both lines intersect each other at (3,-3). So, the solution of given equations is (3,-3) instead of (-3,-3).

Therefore, she is incorrect because the correct solution is (3,-3).