Question

Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?

(1, 0) and (0, –1)
(–2, –3) and (1, 0)
(0, –3) and (1, 0)
(–3, –2) and (0, 1)

Answer 1

The solutions are (-2,-3) and (1,0).

EXPLANATION

The given system has equations:

`y = {x}^(2) + 2x - 3`

and

`y = x - 1`

We equate both equations:

`{x}^(2) + 2x - 3 = x - 1`

`{x}^(2) + 2x - x - 3 + 1 = 0`

`{x}^(2) + x - 2 = 0`

`(x - 1)(x + 2) = 0`

This implies that,

`x = - 2 \: or \: x = 1`

When x=-2 , y=-2-1=-3

When x=1, y=1-1=0

The solutions are (-2,-3) and (1,0)

Answer 2

Second option: (-2,-3) and (1,0)

Explanation:

Given the system of equations
`\left \{ {{y = x^2 + 2x-3} \atop {y = x - 1}} \right.`, you can rewrite them in this form:

`x^2 + 2x-3= x - 1`

Simplify:

`x^2 + 2x-3-x+1=0\\\\x^2+x-2=0`

Factor the quadratic equation. Choose two number whose sum be 1 and whose product be -2. These are: 2 and -1, then:

`(x+2)(x-1)=0\\\\x_1=-2\\\\x_2=1`

Substitute each value of "x" into any of the original equation to find the values of "y":

`y_1= (-2) - 1=-3\\\\y_2=(1)-1=0`

Then, the solutions are:

(-2,-3) and (1,0)