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

Sep 10, 2016

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 $a x + b y = c$ and $b x + a y = d$), 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 $3 x + 2 y = 16$ and $2 x + 3 y = 14$

adding them gives $4 x + 5 y = 30$ 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 $2 x = 8$ or $x = 4$.

And $y = 6 - 4 = 2$

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