solve the following systems?

Question

2x+3y-2x=4
x+3y-3z=4
3x-6y+z= - 3

Answer 1

I assume you meant 2x +3y - 2z = 4 for the top equation.

The simplest way to solve such a system of equations is by row reduction. First use one of the equations to eliminate x from the other two, then use another to eliminate y, and then z. For your example, it is easiest to use the middle equation to eliminate x, since x appears without a coefficient. You would multiply the middle equation by -2 and add it to the top one, and then multiply the middle equation by -3 and add to the bottom. Doing this you get:

-3y +4z = -4
x+3y-3z = 4
-15y + 10z = -15

Now you can use the top equation to elimiate y from the other two to get

-3y + 4z = -4
x+z = 0
-10z = 5

At this point it's probably easiest to just solve for z in the last equation to get z = -1/2, and then the second equation says x = -z = 1/2, and then the top equation says -3y - 2 = -4. Solving for y you get y = 2/3. Then its always good to check your answer by plugging back in.