Question

graph each equation. determine the solution of the system of equations.
x + 4y = 8
3x + 4y = 0
use the graphing tool to graph the system.

Explanation:

Step1: Subtract the two equations

We have the system:
\[

$$\begin{cases} x + 4y = 8 \\ 3x + 4y = 0 \end{cases}$$

\]
Subtract the first equation from the second equation: \((3x + 4y)-(x + 4y)=0 - 8\)
Simplify the left - hand side: \(3x+4y - x - 4y=2x\)
Simplify the right - hand side: \(- 8\)
So we get \(2x=-8\)

Step2: Solve for x

Divide both sides of the equation \(2x = - 8\) by 2: \(x=\frac{-8}{2}=-4\)

Step3: Substitute x into one of the original equations

Substitute \(x = - 4\) into the first equation \(x + 4y=8\), we have \(-4 + 4y=8\)
Add 4 to both sides: \(4y=8 + 4=12\)
Divide both sides by 4: \(y=\frac{12}{4}=3\)

Answer:

The solution of the system of equations is \(x=-4,y = 3\) or the ordered pair \((-4,3)\)