# How do you solve the following system?:  x - 3y = 0 , x = 1/2y + 3

Dec 20, 2015

point of intersection $= \left(\frac{18}{5} , \frac{6}{5}\right)$

#### Explanation:

When you solve a system, you are finding the point(s) at which the two lines intersect. We can solve a system by using elimination or substitution. In this case, we will use substitution.

To solve the system, we need to find the values of $x$ and $y$. First, label your equations.

Equation $1$: $x - 3 y = 0$
Equation $2$: $x = \frac{1}{2} y + 3$

$1.$ Start by substituting equation $2$ into equation $1$ to solve for $y$:

$x - 3 y = 0$

$\left(\frac{1}{2} y + 3\right) - 3 y = 0$

$\left(\frac{1}{2} y + \frac{6}{2}\right) - \frac{6}{2} y = 0$

$\frac{y + 6}{2} - \frac{6}{2} y = 0$

$\frac{y + 6 - 6 y}{2} = 0$

$- 5 y + 6 = 0$

$- 5 y = - 6$

$y = \frac{6}{5}$

$2.$ Now that you have the value of $y$, substitute $y = \frac{6}{5}$ into either equation $1$ or $2$ to find the value of $x$. In this case, we will substitute it into equation $1$:

$x - 3 y = 0$

$x - 3 \left(\frac{6}{5}\right) = 0$

$x - \frac{18}{5} = 0$

$x = \frac{18}{5}$

$\therefore$, the point of intersection is $\left(\frac{18}{5} , \frac{6}{5}\right)$.