# How do you solve the system 4m+7n=0, -5m-3n=0?

Mar 4, 2016

$m = 0$, $n = 0$

#### Explanation:

To solve the system of simultaneous equations $4 m + 7 n = 0$ and −5m−3n=0, we multiply the two with different numbers so as to make coefficient of one variable equal in both.

Hence multiplying first by $5$ and second by $4$, we get

$20 m + 35 n = 0$ and −20m−12n=0.

Now as coefficient of $m$ are same but have opposite sign, add them and we get

$23 n = 0$ i.e. $n = 0$.

Putting this in say first equation, we get

$4 \cdot 0 + 7 n = 0$ or $7 n = 0$ or $n = 0$