Question

Two lines, A and B, are represented by the equations given below!
Line A: y = x - 4
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?

A. (-3,-5), because the point satisfies ONE of the equations

B. (-3,-5), because the point lies between the two axes

C. (-4,-8), because the point satisfies BOTH equations

D. (-4,-8), because the point does not lie on any axis

Answer 1

Answer:

The solutions to the system of equations are:

$y=-8,\:x=-4$

Thus, option C is true because the point satisfies BOTH equations.

Step-by-step explanation:

Given the system of the equations

$\begin{bmatrix}y=x-4\\ y=3x+4\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}y-x=-4\\ y-3x=4\end{bmatrix}$

$y-3x=4$

$-$

$\underline{y-x=-4}$

$-2x=8$

$\begin{bmatrix}y-x=-4\\ -2x=8\end{bmatrix}$

solve for x

$-2x=8$

Divide both sides by -2

$\frac{-2x}{-2}=\frac{8}{-2}$

$x=-4$

$\mathrm{For\:}y-x=-4\mathrm{\:plug\:in\:}x=-4$

$y-\left(-4\right)=-4$

$y+4=-4$

$y=-8$

The solutions to the system of equations are:

$y=-8,\:x=-4$

Thus, option C is true because the point satisfies BOTH equations.