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Contact [7]
3 years ago
8

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

Mathematics
2 answers:
Sonja [21]3 years ago
7 0

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)

Lerok [7]3 years ago
5 0

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)

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