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:

$\begin{gathered} y=\frac{1}{2}x-1 \\ 3x-2y=1 \end{gathered}$

Isolate x from the second equation:

$\begin{gathered} 3x-2y=1 \\ \Rightarrow3x=2y+1 \\ \Rightarrow x=\frac{2y+1}{3} \end{gathered}$

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

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

Solve for y:

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