Question

Find the solution to the system of equations.


\[\begin{cases}
y=-5x+6
\\\\
y=3x-2
\end{cases}\]
\[x= \]
\[y= \]

Answer 1

To solve the system of equations

\[
\begin{cases}
y = -5x + 6 \\
y = 3x - 2
\end{cases}
\]

we can set the two equations for \(y\) equal to each other:

\[
-5x + 6 = 3x - 2
\]

Now, we will solve for \(x\). First, we can add \(5x\) to both sides:

\[
6 = 3x + 5x - 2
\]

This simplifies to:

\[
6 = 8x - 2
\]

Next, we can add \(2\) to both sides:

\[
6 + 2 = 8x
\]
\[
8 = 8x
\]

Now, divide both sides by \(8\):

\[
x = 1
\]

Now that we have the value of \(x\), we can substitute it back into either of the original equations to find \(y\). We’ll use the first equation:

\[
y = -5(1) + 6
\]
\[
y = -5 + 6
\]
\[
y = 1
\]

Thus, the solution to the system of equations is:

\[
x = 1, \quad y = 1
\]

In summary:

\[
x = 1
\]
\[
y = 1
\]