Question

Graph the system of equations on your graph paper to answer the question.

y=−3x+9

y=−x−5

What is the solution for the system of equations?


(9, 4)

(-7, 12)

(7, -12)

(12, -7)

Answer 1

As the point of the intersection of the lines is (7, -12), the solution of the system is

`y=-12,\:x=7`

Please check the attached graph below.

Explanation:

Given the system of the equations

`y=-3x+9;\:y=-x-5`

Check the attached graph below.

It is clear from the graph that the lines intersect at x =7 and y = -12

so the point of the intersection of the lines is (7, -12)

Hence, the solution of the system is

`y=-12,\:x=7`

VERIFICATION BY SOLVING THE SYSTEM OF THE EQUATION

Given the system of the equations

`y=-3x+9;\:y=-x-5`

Solving the system of the equations

`\begin{bmatrix}y=-3x+9\\ y=-x-5\end{bmatrix}`

`\mathrm{Subsititute\:}y=-x-5`

`\begin{bmatrix}-x-5=-3x+9\end{bmatrix}`

Isolate x for
`-x-5=-3x+9`

`-x-5=-3x+9`

`-x-5+5=-3x+9+5`

`2x=14`

`x=7`

`\mathrm{For\:}y=-x-5`

`\mathrm{Subsititute\:}x=7`

`y=-7-5`

`y=-12`

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`y=-12,\:x=7`