Question

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

Answer 1

`x=-7` and `y=-2`

Explanation:

The equations are

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

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

As we have `3x` 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

`-6y-(-4y)=-9-(-13)`

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

or `-2y=4` and `y=-4/2=-2`

Now putting this in (1), we get

`3x-6xx(-2)=-9`

or `3x+12=-9`

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

i.e. `x=-21/3=-7`

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