2x+y-z=5 3x-y+2z=-1X-y-z=0

Question

Can you solve this problem for me.

Answer 1

2x + y - z = 5

3x - y + 2z = -1

x - y - z = 0

There's a great way to do this involving matrix operations but since I'm not sure of your grade level and considering the constraints of the website, I'll do this via substitution using the last equation since all coefficients are 1.

So, x - y -z = 0  ===>  x = y + z

Substituting that in to the remaining 2 equations:

Equation 1: 2(y + z) + y - z = 5    ===> 3y + z = 5

Equation 2: 3(y + z) - y + 2z = -1 ===> 2y + 5z = -1

Here you can multiply either equation by a number that will eliminate one of the variables through addition. I'll use -5 * [Equation 1]

-5*[3y + z = 5] ===> -15y - 5z = -25

Now add that to equation 2:

-15y + 2y - 5z + 5z = -1 + (-25)

-13y = -26 and

y = 2

substituting that value back into equation 1:

3*(2) + z = 5 ===> 6 + z = 5

z = -1

Now to use equation three from above:

x = y + z

x = 2 + (-1) = 1

The solution in (x,y,z) form is then: (1,2,-1)

Always check your answers using those values in the original equations:

2*(1) + 2 - (-1) = 5  ===> 5 = 5

3*(1) - 2 + 2*(-1) = -1 ===> -1 = -1

1 - 2 -(-1) = 0 ===> 0 = 0