# How do you solve the simultaneous equations 4x+5y=0 and 8x-15y=5?

Apr 11, 2018

$x = 0.25$ and $y = - 0.2$

#### Explanation:

For simultaneous equations you have to know 2 rules:
• Same signs subtract
meaning if both equations have the same sign you subtract to cancel out $x \mathmr{and} y$

meaning if both equations have different signs you add to also cancel out $x \mathmr{and} y$

In this case, you will add both equations because they are of different signs

$4 x + 5 y = 0$
$8 x - 15 y = 5$

multiply the first equation by $3$ to cancel out $y$ values by adding

after multiplying you'll have
$12 x + 15 y = 0$
$+$
$8 x - 15 y = 5$
$20 x = 5$
$x = \frac{5}{20}$
$x = 0.25$

Substitute the value of $x$ in either of the equations

$4 x + 5 y = 0$
$4 \left(0.25\right) + 5 y = 0$
$1 + 5 y = 0$
$5 y = - 1$
$y = - \frac{1}{5}$ or $- 0.2$

so $x = 0.25$ and $y = - 0.2$