Question

Could you please provide an example of a system of equations with three variables and show your work?

Answer 1

One example of a system of equations with three variables is 2x + y - 3z = 7, x - 3y + 2z = 5, 4x + 2y + z = 10. To solve this system, you can use the elimination method to eliminate variables one by one and find the values for x, y, and z.

Step-by-step explanation:

One example of a system of equations with three variables is:

2x + y - 3z = 7

x - 3y + 2z = 5

4x + 2y + z = 10

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

1. Multiply equation (1) by 2 and equation (2) by 4 to make the coefficients of x in both equations equal.
2. Subtract equation (1) from equation (2) to eliminate x.
3. Multiply equation (1) by -1 to make the coefficients of x in both equations equal.
4. Add equation (1) to the new equation (3) to eliminate x.
5. Now we have a system of two equations in two variables:

3y - 7z = 3

3y + 3z = 2

Continue solving this system like a regular two-variable system by using substitution or elimination. Once you find the values for y and z, substitute them back into one of the original equations to find the value of x.