Question

How do you solve the system of equations `3x-2y=-21` and `2x+5y=5` by elimination?

Answer 1

You need to make the coefficients of either the `x` or the `y` the same. The better option is to have them with different signs. These are called additive inverses.

Explanation:

`3x` and `2x` can both be made into the LCM `6x`, by multiplying the whole of the first equation by 2 and the whole of the second equation by 3. You would then subtract one equation from the other to eliminate the `x` terms.

However, an easier method which will incur fewer errors is to make both the `y` terms into `10y`. Note that the signs are different.
Multiply the whole of the first equation by 5 and the whole of the second equation by 2. The following two equations will be obtained:

`15x-10y = -105`
`4x+ 10y = 10`
When these two equations are added, the `y` terms are eliminated because they add to give zero. An equation will only one variable is formed .... `19x = -95`
which gives `x= -5`

Simple substitution into either of the original equations gives
`y=3`.

Check the answer by substituting the values `x = -5 and y = 3` into the other equation.