Answer:
(-2, 0)
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{5}{2}x-5\\x-y=-2\end{cases}[/tex]
Rewrite the second equation to make y the subject:
[tex]\implies x-y=-2[/tex]
[tex]\implies x=y-2[/tex]
[tex]\implies y=x+2[/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{5}{2}(0)-5=-5 \implies (0, -5)[/tex]
[tex]x=-4\implies y=-\dfrac{5}{2}(-4)-5=5 \implies (-4,5)[/tex]
Equation 2
[tex]x=0 \implies y=0+2=2 \implies (0,2)[/tex]
[tex]x=5 \implies y=5+2=2 \implies (5,7)[/tex]
From inspection of the graph (see attached), the point of intersection is (-2, 0).
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