Question

Which ordered pair is a solution to the system of equations?Note: Use the substitution method.{x=1/4y+2 and −4x+3y=4 (−1/12, −2/63 )(7/2, 6 )(5/4, 3 )(−1/4, 1 )

Answer 1

Given the system of equations

`\begin{gathered} x=(1)/(4)y+2 \\ -4x+3y=4 \end{gathered}`

Substitute x =1/4y+2 in the second equation

`-4((1)/(4)y+2)+3y=4`

Simplify

`\begin{gathered} -y-8+3y=4 \\ 2y-8=4 \end{gathered}`

Solve for y

`\begin{gathered} 2y-8+8=4+8 \\ 2y=12 \\ (2y)/(2)=(12)/(2) \\ y=6 \end{gathered}`

Then substitute y = 6 in x

`x=(1)/(4)(6)+2=(6)/(4)+2=(7)/(2)`

Answer: (7/2, 6)