Question

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

C. Line
`y = -2x + 3` intersect the line
`y = -x + 6`.

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.

Answer 2

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.