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

Mar 2, 2018

$x = 36$, $y = - 20$

#### Explanation:

We have, $x + y = 16$.............$\left[1\right]$

And also $2 x + 3 y = 12$................$\left[2\right]$

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

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

$x = 36$............$\left[3\right]$ Substitute this value of $x$ into ..$\left[1\right]$

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

substituting these values of $x \mathmr{and} y$ into...... $\left[1\right]$ or$\left[2\right]$ and they should satisfy the equations.