# Question a709f

Apr 29, 2017

x=1/5 ; y=3/10

#### Explanation:

Given: $3 x - 2 y = 0$ equation 1)
$5 x + 10 y = 4$ equation 2)

We will need to multiply one or both of the equations to obtain like terms in the two so we can then add or subtract one equation from the other to eliminate the like terms.

Lets try that one step at a time. We will multiply 1) by $5$:

$3 x - 2 y = 0 \implies 5 \cdot \left(3 x - 2 y = 0\right) \implies 15 x - 10 y = 0$

Then add the new 1) to 2) to eliminate like terms:

$15 x \cancel{- 10 y} = 0$
(5xcancel(+10y)=4)/
$20 x \textcolor{w h i t e}{\ldots \ldots . .} = 4$

$5 x = 1 \implies x = \frac{1}{5}$

$x = \frac{1}{5}$ and using this information we could use either 1) or 2) to solve for $y .$

But we will instead solve for $y$ by elimination as well.

We will multiply 1) by $5$ again:

$3 x - 2 y = 0 \implies 5 \left(3 x - 2 y = 0\right) \implies 15 x - 10 y = 0$

We will also multiply 2) by $3$:

$5 x + 10 y = 4 \implies 3 \left(5 x + 10 y = 4\right) \implies 15 x + 30 y = 12$

Now we need to subtract 2) from 1):

$\cancel{15 x} \textcolor{w h i t e}{\ldots \ldots . .} - 10 y = \textcolor{w h i t e}{\ldots . .} 0$
(cancel(-15x)cancel(+)-30y=-12)/#
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} - 40 y = - 12$

$- 10 y = - 3 \implies y = \frac{3}{10}$

To check the answers we will substitute them back into either $g i v e n$ equation.

$3 x - 2 y = 0$

$3 \left(\frac{1}{5}\right) - 2 \left(\frac{3}{10}\right) = 0$

$\frac{3}{5} - \frac{6}{10} = 0$

$\frac{3}{5} - \frac{3}{5} = 0$