The solution to the system of equations is (2,0)
The equation is given as:
[tex]y = 0.5x - 1[/tex]
The other equation passes through the points (3,1) and (-5,-7).
Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{-7 - 1}{-5 -3}[/tex]
[tex]m = \frac{-8}{-8}[/tex]
[tex]m =1[/tex]
The equation is then calculated as:
[tex]y = m(x -x_1) + y_1[/tex]
So, we have:
[tex]y = 1(x -3) + 1[/tex]
[tex]y = x -3 + 1[/tex]
[tex]y = x -2[/tex]
Substitute x - 2 for y in [tex]y = 0.5x - 1[/tex]
[tex]x- 2 =0.5x - 1[/tex]
Collect like terms
[tex]x-0.5x= 2 - 1[/tex]
[tex]0.5x= 1[/tex]
Divide both sides by 0.5
[tex]x= 2[/tex]
Substitute 2 for x in [tex]y = 0.5x - 1[/tex]
So, we have:
[tex]y = 0.5\times 2 - 1[/tex]
[tex]y = 1 - 1[/tex]
[tex]y = 0[/tex]
So, we have:
[tex](x,y) =(2,0)[/tex]
Hence, the solution to the system of equations is (2,0)
Read more about systems of equations at:
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