Please help!! I need to get this done! Im begging you, brainliest and points!

Solve this system of equations algebraically, SHOW ALL YOUR WORK PLEASE.

Linear Equation: y = -x + 1

Parabolic Equation: y = x2 + x - 2

What are the solutions for this system (this should be 2 ordered pairs)

Solution; ( 1, 0 ), and ( - 3, 4 )

Step-by-step explanation:

See procedure below;

First let us make these two functions ( y = -x + 1 , y = x^2 + x - 2 ) equivalent;

- x + 1  = x^2 + x - 2,

-x - x + 1 + 2 - x^2 = 0,

- 2x + 3 - x^2 = 0,

x^2 + 2x - 3 = 0,

Now factor the simplified equation;

x^2 + 2x - 3 = 0,

( x^2 - x ) + ( 3x - 3 ) = 0,

x ( x - 1 ) + 3 ( x - 1 ) = 0,

( x - 1 )( x + 3 ) = 0,

And solve for x;

x - 1 = 0, and x + 3 = 0,

x = 1, and x = - 3

Now substitute this value of x into the two functions as to receive the y  values for each x - value;

y = - ( 1 ) + 1, y = 0 for x = 1,

y = ( - 3 )^2 - 3 - 2, y = 9 - 3 - 2, y = 4 for x = - 3,

Solution; ( 1, 0 ), and ( - 3, 4 )

step-by-step explanation: