# How do you solve 2x - y = 3 and 3x - y = 4 using substitution?

May 1, 2016

An alternative method of solving them.
$x = 1 \mathmr{and} y = - 1$

#### Explanation:

Both of these equations contain the single variable $y$.
Transpose them to make $y$ the subject.

$y = 3 x - 4$ ....... and ....... $y = 2 x - 3$

Now, because $y = y$, it follows that

.................$3 x - 4 = 2 x - 3$ (giving an equation with one variable)

Solving it gives: $x = 1$

There are now two ways to calculate the value of $y$

$y = 3 \left(1\right) - 4$ = -1 and $y = 2 \left(1\right) - 3$ = -1