Question

Solve the system of linear equations by graphing{y= 2/5x {y= -1/5x +3Graph the equations on the same set of axes.Note: Use different points on each line when plotting the graphs.The solution point is: (_, _)

Answer 1

The solution point is: (5, 2)

Explanation

To solve the system of linear equations we need to graph each line and find the intersection point.

We can graph a line by connecting two points that lie on the line.

Given the line:

`y=(2)/(5)x`

Evaluating it at the x-values x = 0 and x = 5, we get:

`\begin{gathered} y=(2)/(5)\cdot0 \\ y=0 \\ y=(2)/(5)\cdot5 \\ y=2 \end{gathered}`

Then, this line passes through the points (0, 0) and (5,2)

In the case of the line:

`y=-(1)/(5)x+3`

Evaluating it at the x-values x = 0 and x = -5, we get:

`\begin{gathered} y=-(1)/(5)\cdot0+3 \\ y=3 \\ y=-(1)/(5)\cdot(-5)+3 \\ y=1+3 \\ y=4 \end{gathered}`

Then, this line passes through the points (0, 3) and (-5,4)

The graph of the lines is shown in the next picture (y = 2/5x in red and y = -1/5x + 3 in blue):

And the solution to the system of equations is (5, 2)