Question

What ordered pair is a solution of the system of equations y=x^2-x-20 and y=3x-15?

Answer 1

Hey there!!

Equations given :

y = x² - x - 20 -------- ( 1 )

y = 3x - 15 ------------ ( 2 )

Now, lets first solve for the 1st equation ...

... x² - x - 20

We can write -x as -5x + 4x

... x² + 4x - 5x - 20

... x ( x + 4 ) - 5 ( x + 4 )

... ( x - 5 ) ( x + 4 )

y = ( x - 5 ) ( x - 4 )

Now, let's solve the second equation ...

y = 3x - 15

... y = 3 ( x - 5 )

We have two equations, now getting them together..

3 ( x - 5 ) = ( x - 5 ) ( x - 4 )

Divide by x-5 on both sides

3 = x - 4

Add 4 on both sides

x = 7

The value of x is 7

Now substituting this, we get the value of y

We have,

y = 3x - 15

... y = 3(7 ) - 15

... y = 21 - 15

... y = 6

Hence, the ordered pair is ( 7 , 6 )

Hope my answer helps!