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What The first three steps in determining the solution set of the system of equations algebraically are shown. y=x²-x-3

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What The first three steps in determining the solution set of the system of equations algebraically are shown. y=x²-x-3

Question

What
The first three steps in determining the solution set of the
system of equations algebraically are shown.
y=x²-x-3
y=-3x+ 5
0000
Step
Equation
x²-x-3= – 3x+5
0=x²+2x– 8
O = (x-2)(x+4)
2

## Answers ( )

I assume you want the equation to be solved, so this is a quadratic simultaneous equation.

y = x^2-x-3 ——— (1)

y = -3x+5 ——— (2)

Sub (1) into (2)

(This is the first three steps provided)

x^2-x-3 = -3x+5

0 = x^2+2x-8

0 = (x-2)(x+4) ——— (3)

Solve for x in (3):

x-2 = 0

x = 2

x+4 = 0

x = -4

Sub x into (2)

y = -3(2) + 5

y = -1

y = -3(-4) + 5

y = 17

Hence the solution sets are:

x=2, y=-1

x=-4, y=17