Question

This system has one solution. {y=6x−11y=x2+4x−10 what is the y-coordinate of the solution?

Answer 1

i took the test and the answer was

-5

Answer 2

Answer:

y-coordinate of the solution is, -5

Step-by-step explanation:

Given the system of equations:

$y = 6x-11$

$y= x^2+4x-10$

Equate these two equations we have;

$6x-11 = x^2+4x-10$

Subtract 6x from both sides we have;

$-11 = x^2-2x-10$

Add 11 both sides we have;

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

Using the identity rule:

$(a-b)^2 = a^2-2ab+b^2$

then;

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

⇒$(x-1)^2 = 0$

⇒$x-1 = 0$

⇒x = 1

Substitute the value of x in $y = 6x-11$ we have;

$y = 6(1)-11 = 6-11 = -5$

therefore, the  y-coordinate of the solution is, -5