Answer:
(-5, 5)
Step-by-step explanation:
To solve a linear system of equations graphically, graph the given equations and locate where the two lines intersect. The point of intersection is the solution to a system of linear equations.
Given linear system of equations:
[tex]\begin{cases}y=\dfrac{1}{5}x+6\\4x+5y=5\end{cases}[/tex]
Rewrite the second equation to make y the subject:
[tex]\implies 4x+5y=5[/tex]
[tex]\implies 5y=-4x+5[/tex]
[tex]\implies y=-\dfrac{4}{5}x+1[/tex]
To graph a linear equation, find two points on the line by substituting two values of x into the equation. Plot the points and draw a straight line through them.
Equation 1
[tex]x=0 \implies y=\dfrac{1}{5}(0)+6=6 \implies (0,6)[/tex]
[tex]x=5 \implies y=\dfrac{1}{5}(5)+6=7 \implies (5,7)[/tex]
Equation 2
[tex]x=0 \implies y=-\dfrac{4}{5}(0)+1=1 \implies (0,1)[/tex]
[tex]x=5 \implies y=-\dfrac{4}{5}(5)+1=-3 \implies (5,-3)[/tex]
From inspection of the graph (see attached), the point of intersection is (-5, 5).
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