Question

The following system of equations intersects at one point. What is the y-coordinate of this point? y = (1/2)x-13x - 2y = 1

Answer 1

Starting with the system of equations:

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

Isolate x from the second equation:

`\begin{gathered} 3x-2y=1 \\ \Rightarrow3x=2y+1 \\ \Rightarrow x=(2y+1)/(3) \end{gathered}`

Plug in the expression for x from the second equation into the first equation:

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

Solve for y:

`\begin{gathered} \Rightarrow y=(2y+1)/(6)-1 \\ \Rightarrow6y=(2y+1)-6 \\ \Rightarrow6y=2y+1-6 \\ \Rightarrow6y=2y-5 \\ \Rightarrow6y-2y=-5 \\ \Rightarrow4y=-5 \\ \Rightarrow y=-(5)/(4) \end{gathered}`