Question

Y=15x+4y=x2+7x+20 What is the y-coordinate of the solution? Enter your answer in the box. ASAP

Answer 1

y = 64

Explanation:

Given system of equations:

`\begin{cases}y=15x+4\\y=x^2+7x+20\end{cases}`

To find the y-coordinate of the solution to the given system of equations, first solve for x, then substitute the value of x into one of the equations and solve for y.

Set the equations equal to each other and solve for x:

`\begin{aligned}x^2+7x+20&=15x+4\\x^2+7x+20-15x-4&=15x+4-15x-4\\x^2-8x+16&=0\\x^2-4x-4x+16&=0\\x(x-4)-4(x-4)&=0\\(x-4)(x-4)&=0\\(x-4)^2&=0\\\\x-4&=0 \implies x=4\end{aligned}`

Now, substitute x = 4 into one of the equations and solve for y:

`\begin{aligned}x=4 \implies y&=15(4)+4\\y&=60+4\\y&=64\end{aligned}`

Therefore, the y-coordinate of the solution to the given system of equations is y = 64.