Question

What is the x-value of the solution to the system that includes y = x^2 + 2x – 2 and y = 5x – 4.25?

Answer 1

Answer: We are going to solve the following systems of equations.

`\begin{gathered} y=x^2+2x-2\rightarrow(1) \\ y=5x-4.25\rightarrow(2) \end{gathered}`

substituting equation (2) in (1) gives:

`\begin{gathered} 5x-4.25=x^2+2x-2 \\ \therefore\rightarrow \\ -x^2+3x-2.25=0 \\ x=(3)/(2) \end{gathered}`
`\begin{gathered} \therefore\rightarrow \\ y=5((3)/(2))-4.25=7.5-4.25=3.25 \end{gathered}`
`\begin{gathered} \therefore\rightarrow \\ x=(3)/(2) \\ y=3.25 \end{gathered}`