# Solve the following system of equations. 2x_1−x_2−x_3=−3 3x_1+2x_2+x_3=13 x_1+2x_2+2x_3=11 (x_1, x_2, x_3) =

Solve the following system of equations.
$2{x}_{1}-{x}_{2}-{x}_{3}=-3$
$3{x}_{1}+2{x}_{2}+{x}_{3}=13$
${x}_{1}+2{x}_{2}+2{x}_{3}=11$
$\left({x}_{1},{x}_{2},{x}_{3}\right)=$
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Theodore Schwartz

Step 1
Let x_1=x , x_2=y and x_3=z
So, the equations are:
2x-y-z=-3
3x+2y+z=13
x+2y+2z=11
Step 2
Let use eliminate z first. Add first two equations. That gives 5x+y=10
Step 3
Multiply first equation by 2 and add it to the third equation.
$2\left(2x-y-z=-3\right)⇒4x-2y-2z=-6$
So we get 5x=5
So, $x=\frac{5}{5}=1$
Step 4
Here we plug x=1 and find y
5(1)+y=10
Or, 5+y=10
Or, y=5
Step 5
In 2x-y-z=-3 we plug x=1 and y=5 and find z
2(1)-5-z=-3
Or, 2-5-z=-3
Or, -3-z=-3
Or, z=0
Result: $\left({x}_{1},{x}_{2},{x}_{3}\right)=\left(1,5,0\right)$

Jeffrey Jordon