How do you solve the system 4x-7y=9 and y=x-3 using substitution?

May 19, 2015

You isolate one variable in one equation and substitute the value you find in the other equation.

You can choose any of the variables in any of the equations, but don't forget to substitute its value in the other one!

One tip is to isolate the one you find easier to manipulate, without fractions, for example, if possible.

Let's, then, isolate $y$ in the second equation:

$y = x - 3$

Now, let's substitute its value in the first:

$4 x - 7 \left(x - 3\right) = 9$

You see that now we have only $x$ and numbers, so we will end up finding $x$.

$4 x - 7 x + 21 = 9$
$- 3 x = - 12$
$x = 4$

Now we've found $x$, we can substitute it in the value of $y$:

$y = x - 3$
$y = 4 - 3$
$y = 1$

So, $x = 4$ and $y = 1$