# How do you solve the system 5x - y = 3 and -10x + 2y = -6?

Jun 30, 2017

See a solution process below:

#### Explanation:

Both of these equations are almost in the Standard Form for linear equations. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.

We can get the second equation closer to Standard Form by multiplying both sides of the equation by $- 1$:

$- 1 \left(- 10 x + 2 y\right) = - 1 \cdot - 6$

$10 x - 2 y = 6$

Now, we can divide each side of the equation by $2$ to get this equation into true standard form:

$\frac{10 x - 2 y}{2} = \frac{6}{2}$

$5 x - y = 3$

These equations are actually the same equation. Therefore, the solution to this is they have all points in common.