Question

What are the x-coordinates of the solutions to this system of equations?

x2 + y2 = 25
y = 2x - 5

A) -4 and 0

B) 4 and 0

C) -3 and -5

D) 3 and -5

Answer 1

Option B is correct

the values of x-coordinates are 4 and 0

Explanation:

Given the system of equations:

`x^2+y^2=25` .....[1]

`y=2x-5` .....[2]

Substitute equation [2] into [1] we have;

`x^2+(2x-5)^2 = 25`

⇒
`x^2+4x^2-20x+25=25`

Subtract 25 from both sides we have;

`x^2+4x^2-20x=0`

Combine like terms;

`5x^2-20x=0`

⇒
`5x(x-4)=0`

By zero product property we have;

x = 0 and x-4 = 0

⇒x = 0 and x = 4

Therefore, the values of x are 4 and 0

Answer 2

x² + y² = 25
y = 2 x - 5
---------------
x² + ( 2 x - 5 )² = 25
x² + 4 x² - 20 x + 25 = 25
5 x² - 20 x = 25 - 25
5 x ( x - 4 ) = 0
x 1 = 0 and x 2 = 4
Answer: B ) 4 and 0