# How do you solve the system of equations: 2x + y = 1 and 4x+2y = 5?

Aug 23, 2015

$\left\{\begin{matrix}x = \emptyset \\ y = \emptyset\end{matrix}\right.$

#### Explanation:

Even without doing any calculations, you can say that this system of equations has no solution.

That is the case because multiplying the first equation by $2$ will get you

$2 x + y = 1 | \cdot \left(2\right)$

$4 x + 2 y = 2$

The two equations will thus be

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

The left sides of the two equations are equal, but the right sides are not. If you try to replace the left side of the second equation by using the first equation, you will get

$2 \ne 5$

Remember that the solution of a system of equations represents the point in space where the two lines described by the equations intersect.

You're essentially dealing with two parralel lines, which means that the system of equations will have no solution.

graph{(4x+2y-2)(4x+2y-5)=0 [-10, 10, -5, 5]}