Question

How do you solve the following system: `x + y = 16, 2x + 3y = 12`?

Answer 1

`x=36`, `y=-20`

Explanation:

We have, `x+y=16`.............`[1]`

And also `2x+3y=12`................`[2]`

From `[1]` subtracting `x` from both sides, `y=16-x` and substituting this value for `y` into `[2]` we obtain.......

`2x+3[16-x]=12`, and so after expanding the bracket we get
`2x+48-3x=12`, after arranging and collecting like terms,

`x=36`............`[3]` Substitute this value of `x` into ..`[1]`

`36+y=16` and so `y=-20`. You can check these answers by

substituting these values of `x and y` into...... `[1]` or`[2]` and they should satisfy the equations.