Question

How do you solve the following system?: `-4x -3y =5, x -2y = -15`

Answer 1

`x = -5 and y = 5`

Explanation:

`-4x- 3y = 5 - - - eqn1`

`x - 2y = -15 - - - eqn2`

From the `eqn1` rearrange the equation..

`-4x - 3y = 5`

Multiplying through by minus`(-)`;

`-(-4x - 3y = 5)`

`4x + 3y = -5 - - - eqn1`

Now solving simultaneously..

`4x + 3y = -5 - - - eqn1`

`x - 2y = -15 - - - eqn2`

Using Elimination Method..

Multiplying `eqn1` by `1` and `eqn2` by `4` respectively..

`1(4x + 3y = -5)`

`4(x - 2y = -15)`

`4x + 3y = -5 - - - eqn3`

`4x - 8y = -60 - - - eqn4`

Subtracting `eqn4` from `eqn3`

`(4x - 4x) + (3y - (-8y) = -5 - (-60)`

`0 + 3y + 8y = -5 + 60`

`11y = 55`

`y = 55/11`

`y = 5`

Substituting the value of `y` into `eqn2`

`x - 2y = -15 - - - eqn2`

`x - 2(5) = -15`

`x - 10 = -15`

`x = -15 + 10`

`x = -5`

Therefore;

`x = -5 and y = 5`