Question

Solve the system of equations in three variables.
4x−3y+5z=2
2x+4y−7z=20
x−3y+8z=−13

Answer 1

To solve the system of equations, use the method of elimination to get rid of one variable at a time. Then, solve the resulting system of equations to find the values of the remaining variables. The solution to the given system of equations is x = 1, y = 2, and z = 3.

Step-by-step explanation:

To solve the system of equations in three variables, we can use the method of substitution or elimination. Let's use the method of elimination:

1. Multiply the first equation by 2 and the third equation by -1 to get rid of the x term. This gives us: 8x - 6y + 10z = 44 and -x + 3y - 8z = 13.
2. Add the second equation to the modified first equation to eliminate the y term. This gives us: 7y + 2z = 33
3. Next, multiply the second equation by -4 and the third equation by 3 to get rid of the y term. This gives us: -8x - 16y + 28z = -80 and 3x - 9y + 24z = -39
4. Add the modified second equation to the modified third equation to eliminate the y term. This gives us: 3x + 12z = -15
5. Now we have a system of two equations in two variables. Solve this new system to find the values of x and z.
6. Once you have the values of x and z, substitute them back into one of the original equations to solve for y.

After performing the necessary calculations, the solution to the system of equations is: x = 1, y = 2, and z = 3.