Answer:
(4, -1)
Step-by-step explanation:
Given equations:
[tex]y=\dfrac{3}{2}x-7[/tex]
[tex]y=-x+3[/tex]
To plot the lines, find 2 points for each equation and draw a straight line through them.
[tex]\textsf{For }\quad y=\dfrac{3}{2}x-7:[/tex]
[tex]x=0 \implies y=\dfrac{3}{2}(0)-7=-7 \implies (0,-7)[/tex]
[tex]x=6 \implies y=\dfrac{3}{2}(6)-7=2 \implies (6,2)[/tex]
[tex]\textsf{For }\quad y=-x+3:[/tex]
[tex]x=0 \implies y=-(0)+3=3 \implies (0,3)[/tex]
[tex]x=6 \implies y=-(6)+3=-3 \implies (6,-3)[/tex]
The solution to the system of equations is the point of intersection:
Therefore, from inspection of the graph, the solution is (4, -1)
