Question

How do you solve `3x + 2y = 16` and `2x + 3y = 14`?

Answer 1

Solution is `x=4` and `y=2`

Explanation:

When we have such linear equations, where we have addition only and coefficients of `x` and `y` reversed (i.e. of the type `ax+by=c` and `bx+ay=d`), we can just add the two equations to get one equation and then subtract one from other to get another, which when simplified become equations of the type `x+y=m` and `x-y=n` and easier to solve,

Here we have `3x+2y=16` and `2x+3y=14`

adding them gives `4x+5y=30` or `x+y=6`

subtracting second from first gives `x-y=2`

Now as `x+y=6` and `x-y=2`, adding them we get `2x=8` or `x=4`.

And `y=6-4=2`

Hence solution is `x=4` and `y=2`