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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.

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Answer:

Line[tex]y=-2x+3[/tex] intersects line [tex]y=x-5[/tex]

Step-by-step explanation:

We are given that

[tex]y=-2x+3[/tex]

[tex]y=x-5[/tex]

Subtract one equation from other then we get

[tex]-3x+8=0[/tex]

[tex]3x=8[/tex]

[tex]x=\frac{8}{3}[/tex]

Substitute the value of x in first equation then we get

[tex]y=-2(\frac{8}{3})+3=-\frac{16}{3}+3=-\frac{-7}{3}[/tex]

Hence, the solution [tex](\frac{8}{3},-\frac{7}{3})[/tex] is the intersection point of two line  equations .

Answer:Line[tex]y=-2x+3[/tex] intersects line [tex]y=x-5[/tex]

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