# How do you solve y = 3x - 4 and 2x - y = 1?

The solution is $\left(x , y\right) = \left(3 , 5\right)$

#### Explanation:

Hence you have two linear equations we have that

$y = 3 x - 4$ and $y = 2 x - 1$

since the first parts are equal so the second are

$3 x - 4 = 2 x - 1 \implies x = 3$ and $y = 2 \cdot 3 - 1 = 5$

Sep 25, 2015

$x = 3$
$y = 5$

#### Explanation:

$y = 3 x - 4$ $\Rightarrow$ 1st equation
$2 x - y = 1$ $\Rightarrow$ 2nd equation

Since $y$ is already the subject of the first equation, all you need to do is substitute $y = 3 x - 4$ into the 2nd equation!

So,

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

Expand the brackets.

$2 x - 3 x + 4 = 1$

Which gets you:

$- x + 4 = 1$

Move the 4 over so $x$ becomes your subject.

$- x = - 4 + 1$
$- x = - 3$

Switch them over so your $x$ is positive!

$3 = x$

To find $y$, just substitute $x = 3$ into either the 1st of 2nd equation.

So,

$y = 3 \left(3\right) - 4$
$y = 9 - 4$
$y = 5$

To check:
Substitute the values of $x$ and $y$ back into the equation. You will get the same answer.