Question

5x-y=19 and x-y=-1
substitution

Answer 1

Assuming you want to solve for x and y:

The easiest place to start is \(x - y = -1\). You can isolate \(x\) by moving \(y\) to the right: \(x = -1 + y = y - 1\).

Then, you can substitute for x in \(5x - y = 19\):

\[\begin{align}
5x - y &= 19\\
5(y - 1) - y &= 19\\
5y - 5 - y &= 19\\
4y - 5 &= 19\\
4y &= 24\\
y &= 6
\end{align}\]

Now that you've determined the value of \(y\), you can plug into the first equation to get the value of \(x\):

\[x = y - 1 = 6 - 1 = 5\]

You can then double-check that both of the equations are valid by plugging in the two values you just found for \(x\) and \(y\):

\[5 - 6 = -1\]
\[5\cdot 5 - 6 = 25 - 6 = 19\]