Question

This system has one solution.

y=8x−14
y=x2+4x−10
What is the y-coordinate of the solution?

Answer 1

y = 2

Explanation:

`y=8x-14\qquad(1)\\y=x^2+4x-10\qquad(2)\\\\\text{compare equations}\\\\x^2+4x-10=8x-14\qquad\text{subtract 8x from both sides}\\\\x^2-4x-10=-14\qquad\text{add 14 to both sides}\\\\x^2-4x+4=0\\\\x^2-2x-2x+4=0\\\\x(x-2)-2(x-2)=0\\\\(x-2)(x-2)=0\\\\(x-2)^2=0\iff x-2=0\qquad\text{add 2 to both sides}\\\\x=2\\\\\text{Put the value of x to (1)}:\\\\y=8(2)-14=16-14=2`