# How do you solve the system of equations: x+y+z = 105, 10y-z = 11, 2x-3y = 7 ?

Sep 27, 2016

$x = 17$, $y = 9$ and $z = 79$

#### Explanation:

Given:

$x + y + z = 105$

$10 y - z = 11$

$2 x - 3 y = 7$

Add the first two equations together to eliminate $z$ and get:

$x + 11 y = 116$

Multiply this equation by $2$ to get:

$2 x + 22 y = 232$

Subtract the original third equation to eliminate $x$ and get:

$25 y = 225$

Divide both sides by $25$ to get:

$\textcolor{b l u e}{y = 9}$

Substitute this value of $y$ into the third equation to get:

$2 x - 27 = 7$

Add $27$ to both sides to get:

$2 x = 34$

Divide both sides by $2$ to get:

$\textcolor{b l u e}{x = 17}$

Substitute the values for $x$ and $y$ into the first equation to get:

$17 + 9 + z = 105$

Subtract $26$ from both sides to get:

$\textcolor{b l u e}{z = 79}$