Solve the system by elimination. -2x + 2y + 3z = 0 -2x - y + z = -3 2x + 3y + 3z = 5( sow your work)

These are three linear equations in in three variables.






To solve this by elimination, we are going to add equation (3) to (1) and (2) simultaneously.

First equation (3) + (1)

This implies that



Next let's add equation (2) and (3)

This implies that



Equations (4) and (5) are simultaneous linear equation in two variables.

Equation (4) ×2

This implies that


Also equation (5) ×5

This implies that


Now equation (7) - (6) gives



Substitute

in equations (6) or (7) and solve for y.

So using equation (6),





Now plug in z=0 and y=1 into (3) or any other containing the three variables and solve for x.






Hence