Question

Solve the system by elimination. need work to be shown

Answer 1

Answer:

x=1, y=1, z=0

Step-by-step explanation:

System of Equations

We are required to solve the system of equations by elimination:

$\left\{\begin{matrix}-2x+2y+3z=0\qquad [1]\\-2x-y+z=-3 \qquad [2]\\2x+3y+3z=5 \qquad [3]\end{matrix}\right$

Adding [1] and [3], and subtracting [1] and [2]:

$\left\{\begin{matrix}5y+6z=5\qquad [4]\\3y+2z=3\qquad [5] \end{matrix}\right.$

Multiplying [5] by -3 and adding to [4]:

$-4y=-4$

Solving:

$y = -4 / (-4) = 1$

$y=1$

Substituting into [5]:

$5(1)+6z=5$

Simplifying:

$6z = 0$

z=0

Substituting into [3]

$2x+3(1)+3(0)=5$

Operating:

$2x+3=5$

$2x = 2$

$x = 2/2=1$

x=1

The solution is

x=1, y=1, z=0