Question

(08.02)Which description best describes the solution to the following system of equations?

y = −2x + 3
y = −x + 6

A. Lines y = −2x + 3 and y = −x + 6 intersect the x-axis.
B. Lines y = −2x + 3 and y = −x + 6 intersect the y-axis.
C. Line y = −2x + 3 intersects the line y = −x + 6.
D. Line y = −2x + 3 intersects the origin.

Answer 1

I believe it's C. It's the most informative and they intersect at (-3, 9)

Answer 2

Line y = −2x + 3 intersects the line y = −x + 6 at (-3,9)

C is correct

Explanation:

Given:

`y=-2x+3`

`y=-x+6`

We are given system of equation and need to solve.

First we find the solution of system of equation and then check the options.

Using substitution method to find x and y

`-2x+3=-x+6`

`-x=6-3`

`x=-3`

Put x=-3 into y=-2x+3

y=-2(-3) + 3 = 9

Point of Intersection: (-3,9)

Hence, The system of equation intersect at (-3,9).