Question

Solve the system of equations for the variables:

x+2y−z=3
x+y−2z=−1
​


a) x=1,y=2,z=−2
b) x=−1,y=2,z=3
c) x=3,y=−1,z=2
d) x=2,y=−2,z=1

Answer 1

To solve the system of equations, we can use the method of substitution. We can solve one equation for one variable and substitute it into the other equation. The correct answer is option d) x=2, y=-2, z=1.

Step-by-step explanation:

To solve the system of equations, we can use the method of substitution. We can start by solving one of the equations for one variable and substituting it into the other equation. Let's solve the second equation for x:

x + y - 2z = -1

x = 1 + 2z - y

Now substitute this expression for x in the first equation:

(1 + 2z - y) + 2y - z = 3

3z - y + 1 = 3

3z - y = 2

Now we have a new equation with only two variables. We can solve this equation together with the second equation for y and z. Subtract the second equation from the modified first equation:

3z - y - (y - 2z) = 2 - (-1)

3z - y - y + 2z = 2 + 1

5z - 2y = 3

Now, let's solve this equation together with the second equation:

5z - 2y = 3

x + y - 2z = -1

We can use any method like substitution or elimination to solve these equations.

The correct answer is option d) x=2, y=-2, z=1.