# How can we solve the simultaneous equations 3x-6y=-9 and 3x-4y=-13?

Feb 2, 2017

$x = - 7$ and $y = - 2$

#### Explanation:

The equations are

$3 x - 6 y = - 9$ ................................(1)

$3 x - 4 y = - 13$ ................................(2)

As we have $3 x$ in both the equations, system of equations can be solved by eliminating this term, which can be done by subtracting equation (2) from (1). Doing this, we get

$- 6 y - \left(- 4 y\right) = - 9 - \left(- 13\right)$

or $- 6 y + 4 y = - 9 + 13$

or $- 2 y = 4$ and $y = - \frac{4}{2} = - 2$

Now putting this in (1), we get

$3 x - 6 \times \left(- 2\right) = - 9$

or $3 x + 12 = - 9$

or $3 x = - 9 - 12 = - 21$

i.e. $x = - \frac{21}{3} = - 7$

Hence, $x = - 7$ and $y = - 2$