Question

The first three steps in determining the solution set of the system of equations algebraically are shown.

Answer 1

In order to solve the system of equations algebraically you have to follow those steps

we have

$y=x^{2}-x-3$ ------> equation A

$y=-3x+5$ -------> equation B

Step 1

Equate the equation A and equation B

$x^{2}-x-3=-3x+5$

$x^{2}-x-3+3x-5=0$

$x^{2}+2x-8=0$

Step 2

Convert the quadratic equation in factored form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2}+2x=8$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$x^{2}+2x+1=8+1$

$x^{2}+2x+1=9$

Rewrite as perfect squares

$(x+1)^{2}=9$

Square root both sides

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

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

$x1=-1+3=2$

$x2=-1-3=-4$

Step 3

Find the values of y

Substitute the value of x in the equation B

For $x=2$

$y=-3*2+5=-1$

For $x=-4$

$y=-3*(-4)+5=17$

therefore

the answer is

$(2,-1)$ and $(-4,17)$

Answer 2

Your answer is (2,-1), (-4,17).