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

Question

shadowfiend · Answer

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 $y$:

$$5 - 6 = -1$$
$$5\cdot 5 - 6 = 25 - 6 = 19$$