# How do solve the following linear system?:  2x - 4y =3, 2x - 5y=3 ?

Mar 16, 2018

$\left(1.5 , 0\right)$

#### Explanation:

So first you can set up your linear system to the following:

$\left\{\begin{matrix}2 x - 4 y = 3 \\ 2 x - 5 y = 3\end{matrix}\right.$

Do this because it is visually easier to simplify the next couple steps.

For the simplification part, I will be using the elimination method on the $x$ variables so that we can obtain a $y$ variable answer.

Multiply the top equation in the linear system by $- 1$

$- 1 \left(2 x - 4 y = 3\right)$
$2 x - 5 y = 3$

You should get the following when simplified:

$\left\{\begin{matrix}- 2 x + 4 y = - 3 \\ 2 x - 5 y = 3\end{matrix}\right.$

Next, add the equations together going vertically making sure to add only to the corresponding term.

The $x$ values and the numerical values should be equal to $0$ when this is done correctly and you should be left with the following:

$- y = 0$

Then simplify by dividing the $- 1$ coefficient from $y$:

$y = 0$

Then you plug the $y$ value back into one of the original equations:

$2 x - 4 \left(0\right) = 3$

Then simplify:

$2 x = 3$

Divide the $2$ coefficient from the $x$ and you should be just left with

$x = \frac{3}{2} = 1.5$

Finally, you plug them into a coordinate point that indicates when the two equations intersect:

$\left(1.5 , 0\right)$