Question

A system of linear equations includes the line that is created by the equation y = 0. 5 x minus 1 and the line through the points (3, 1) and (â€"5, â€"7), shown below. On a coordinate plane, points are at (negative 5, negative 7) and (3, 1). What is the solution to the system of equations? (â€"6, â€"4) (0, â€"1) (0, â€"2) (2, 0).

Answer 1

The solution to the system of equations is (2,0)

The equation is given as:

$y = 0.5x - 1$

The other equation passes through the points (3,1) and (-5,-7).

Start by calculating the slope (m)

$m = \frac{y_2 - y_1}{x_2 -x_1}$

So, we have:

$m = \frac{-7 - 1}{-5 -3}$

$m = \frac{-8}{-8}$

$m =1$

The equation is then calculated as:

$y = m(x -x_1) + y_1$

So, we have:

$y = 1(x -3) + 1$

$y = x -3 + 1$

$y = x -2$

Substitute x - 2 for y in $y = 0.5x - 1$

$x- 2 =0.5x - 1$

Collect like terms

$x-0.5x= 2 - 1$

$0.5x= 1$

Divide both sides by 0.5

$x= 2$

Substitute 2 for x in $y = 0.5x - 1$

So, we have:

$y = 0.5\times 2 - 1$

$y = 1 - 1$

$y = 0$

So, we have:

$(x,y) =(2,0)$

Hence, the solution to the system of equations is (2,0)

Read more about systems of equations at:

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