Question

B) Solve the following and find x, y and z

X - y + z = 10
3x + y + 2z = 34
-5x + 2y – z = -14

Answer 1

To solve the system of equations, we can use the method of elimination by adding or subtracting the equations to eliminate one variable at a time. The solution to the system of equations is x = 6, y = 5, and z = 4.

Step-by-step explanation:

To solve the system of equations:

X - y + z = 10
3x + y + 2z = 34
-5x + 2y – z = -14

We can use the method of substitution or elimination. Here, we will use the method of elimination:

1. Add the first equation and the second equation to eliminate y: (X - y + z) + (3x + y + 2z) = 10 + 34. Simplify: 4x + 3z = 44
2. Add the first equation and the third equation to eliminate y: (X - y + z) + (-5x + 2y - z) = 10 + (-14). Simplify: -4x + 3z = -4
3. Solve the system of equations 4x + 3z = 44 and -4x + 3z = -4
4. Subtract the second equation from the first equation: (4x + 3z) - (-4x + 3z) = 44 - (-4). Simplify: 8x = 48. Divide by 8, x = 6.
5. Substitute the value of x into one of the original equations to find z. Using the first equation: 6 - y + z = 10. Simplify: -y + z = 4. Let's call this Equation A.
6. Add Equation A and the second equation to eliminate y: (-y + z) + (3(6) + y + 2z) = 4 + 34. Simplify: 8z = 34.
7. Divide by 8, z = 4.
8. Substitute the values of x = 6 and z = 4 into one of the original equations to find y. Using the third equation: -5(6) + 2y - 4 = -14. Simplify: 2y = -14 + 24. Simplify: 2y = 10. Divide by 2, y = 5.

Therefore, the solution to the system of equations is x = 6, y = 5, and z = 4.