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Which description best describes the solution to the following system of equations? y = −2x + 3 y = −x + 6

ALines y = −2x + 3 and y = −x + 6 intersect the x-axis.
BLines y = −2x + 3 and y = −x + 6 intersect the y-axis.
CLine y = −2x + 3 intersects the line y = −x + 6.
DLine y = −2x + 3 intersects the origin.

Verified Answer :

nobillionaireNobley

The solution of any two system of equations is the point of intersection of the two lines represented by the equations.
Hence, the solution to the system of equations: y = −2x + 3 and y = −x + 6
is line y = −2x + 3 intersects the line y = −x + 6.

Answer:

C. Line \(y = -2x + 3\) intersect the line \(y = -x + 6\).

Step-by-step explanation:

We are given that,

The system of equations is \(y = -2x + 3\) and \(y = -x + 6\).

Subtracting the equations gives us -x=3 i.e. x= -3.

Substituting the value of x in any equation, we get,

\(y = -x + 6\) implies \(y = -(-3)+ 6\) i.e. y = 3+6 i.e. y= 9.

Thus the solution of the equations is x= -3 and y= 9.

Plotting the equations, we see that,

The graphs of the equations intersect at the point (-3,9).

Hence, both lines intersect each other.

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