Question

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

Answer 1

For the solution(s) to exist the equations must be equal to each other.  Thus we can say y=y which means:

x^2+2x-3=x-1  subtract x from both sides

x^2+x-3=-1  add 1 to both sides

x^2+x-2=0  now factor

(x+2)(x-1)=0, so there are two solutions:

x=-2 and 1, to find the corresponding y values we can use y=x-1

y(-2)=-3 and y(1)=0 so the two solutions are the points:

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

Answer 2

The solutions of the graphed system of equations, y = x² + 2x – 3 and y = x – 1 are B. (–2, –3) and (1, 0)

Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

Let us now tackle the problem!

Given :

$y = x^2 + 2x -3$

$y = x - 1$

To get a solution from the two equations above, it can be done with the following substitution method:

$y = y$

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

$x^2 + 2x - x -3 + 1 = 0$

$x^2 + 2x - x - 2 = 0$

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

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

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

x = -2 or x = 1

For x = - 2 :

$y = x - 1$

$y = -2 - 1$

$y = -3$

∴ The solution is ( -2 , -3 )

For x = 1 :

$y = x - 1$

$y = 1 - 1$

$y = 0$

∴ The solution is ( 1 , 0 )

Learn more

• Solving Quadratic Equations by Factoring : brainly.com/question/12182022
• Determine the Discriminant : brainly.com/question/4600943
• Formula of Quadratic Equations : brainly.com/question/3776858

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number