Question

on your own paper graph the following equations. describe the graphs and give a solution to the system of equations -2x - 5y = 20 y = 4/5 x + 2

Answer 1

Please check the explanation.

Explanation:

Given the system of equations

`\begin{bmatrix}-2x-5y=20\\ y=(4)/(5)x+2\end{bmatrix}`

Please check the attached graph.

On the attached diagram:

The blue line represents the line -2x - 5y = 20

The red line represents the line y = 4/5x + 2

It is clear from the graph that both the graphs meet or intersect each other at the point (-5, -2).

In other words,

(x, y) = ( -5, -2) is the point of intersection of the two lines.

We know that the point of intersection of the two lines is the solution of the system of equations.

Therefore, the solution to the system of equations will be:

(x, y) = ( -5, -2)

The solution to the system of equations using the elimination method:

Given the system of equations

`\begin{bmatrix}-2x-5y=20\\ y=(4)/(5)x+2\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}-2x-5y=20\\ -(4)/(5)x+y=2\end{bmatrix}`

Multiply -2x - 5y = 20 by 2: -4x-10y=40

Multiply y = 4/5x + 2 by 5: -4x+5y=10

so

`\begin{bmatrix}-4x-10y=40\\ -4x+5y=10\end{bmatrix}`

now subtracting

`-4x+5y=10`

`-`

`\underline{-4x-10y=40}`

`15y=-30`

solve 15y = -30 for y

`15y=-30`

Divide both sides by 15

`(15y)/(15)=(-30)/(15)`

`y=-2`

For -4x-10y=40, plug in y = -2

`-4x-10\left(-2\right)=40`

`-4x+20=40`

simplify

`-4x=20`

divide both sides by -4

`(-4x)/(-4)=(20)/(-4)`

Simplify

`x=-5`

Therefore,

The solution to the system of equations will be:

(x, y) = ( -5, -2)