Question

Consider the following system of equations:

y = −2x + 3
y = x − 5

Which description best describes the solution to the system of equations?

Lines y = −2x + 3 and y = 3x – 5 intersect the x-axis.

Line y = −2x + 3 intersects line y = x − 5.

Lines y = −2x + 3 and y = 3x − 5 intersect the y-axis.

Line y = −2x + 3 intersects the origin.

Answer 1

THE answer is B. Line y = −2x + 3 intersects line y = x − 5.

Explanation:

(I got it correct on the quiz)

PROOF:

Answer 2

Line
`y=-2x+3` intersects line
`y=x-5`

Explanation:

We are given that

`y=-2x+3`

`y=x-5`

Subtract one equation from other then we get

`-3x+8=0`

`3x=8`

`x=(8)/(3)`

Substitute the value of x in first equation then we get

`y=-2((8)/(3))+3=-(16)/(3)+3=-(-7)/(3)`

Hence, the solution
`((8)/(3),-(7)/(3))` is the intersection point of two line equations .

Answer:Line
`y=-2x+3` intersects line
`y=x-5`