Answer
The solution point is: (5, 2)
Step-by-step 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:
[tex]y=\frac{2}{5}x[/tex]
Evaluating it at the x-values x = 0 and x = 5, we get:
[tex]\begin{gathered} y=\frac{2}{5}\cdot0 \\ y=0 \\ y=\frac{2}{5}\cdot5 \\ y=2 \end{gathered}[/tex]
Then, this line passes through the points (0, 0) and (5,2)
In the case of the line:
[tex]y=-\frac{1}{5}x+3[/tex]
Evaluating it at the x-values x = 0 and x = -5, we get:
[tex]\begin{gathered} y=-\frac{1}{5}\cdot0+3 \\ y=3 \\ y=-\frac{1}{5}\cdot(-5)+3 \\ y=1+3 \\ y=4 \end{gathered}[/tex]
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)
