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

Answer:

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.

Step-by-step 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 $-x-5=-3x+9$

$-x-5=-3x+9$

$-x-5+5=-3x+9+5$

$2x=14$

$x=7$

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

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

$y=-7-5$

$y=-12$

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

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