Question

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

Answer 1

Answer:

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

Step-by-step 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)

Answer 2

ANSWER

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)