Final answer:
To solve the system by elimination, multiply the first equation by -2 and the second equation by 2 to make the coefficients of x cancel out. When you solve for y, you find y = 0. Substitute this value back into either equation to solve for x and z.
Step-by-step explanation:
To solve the system by elimination, we can multiply the first equation by -2 and the second equation by 2 to make the coefficients of x cancel out. This gives us:
-4x + 4y - 6z = 0
4x + 4y + 6z = 0
Adding these two equations together eliminates the x terms:
8y = 0
Dividing both sides by 8 gives us:
y = 0
Now we can substitute the value of y back into either of the original equations to solve for x and z.