Question

Solve the system of three equations. 2x-3y=4 3y+2z=2 x-z=-5

Answer 1

To solve the given system of equations, substitution and algebraic manipulation are used to find values for x, y, and z. The final solution is x = -1, y = -2, and z = 4.

Step-by-step explanation:

The goal is to solve the system of three equations:

1. 2x - 3y = 4
2. 3y + 2z = 2
3. x - z = -5

First, from the third equation, we can express x in terms of z:

1. x = z - 5

Next, we substitute the expression for x into the first equation:

1. 2(z - 5) - 3y = 4

Now, we solve this new equation for y:

1. 2z - 10 - 3y = 4
2. -3y = 4 - 2z + 10
3. y = (2z - 14)/3

We then substitute this expression for y into the second equation:

1. 3((2z - 14)/3) + 2z = 2
2. 2z - 14 + 2z = 2
3. 4z = 16
4. z = 4

With the value of z found, we go back to the equations for x and y:

1. x = 4 - 5
2. x = -1
3. y = (2(4) - 14)/3
4. y = (8 - 14)/3
5. y = -6/3
6. y = -2

Thus, the solution to the system of equations is x = -1, y = -2, z = 4.