Question

Solve the system of linear equations for the requested variables:

x + y + 2z = 8
X - Y - 2z = -6
X-y + 2z = 2

Answer 1

To solve the system of linear equations, you can use the method of elimination. Start by adding the first and second equations to eliminate y. Then, substitute the value of x into one of the equations to find y and z. Finally, substitute the values of x and z back into one of the equations to find y.

Step-by-step explanation:

To solve the system of linear equations:

x + y + 2z = 8

x - y - 2z = -6

x - y + 2z = 2

1. Start by eliminating variables using addition/subtraction.
2. Add the first equation with the second equation to eliminate y: (x + y + 2z) + (x - y - 2z) = 8 + (-6)
3. This simplifies to: 2x = 2
4. Divide both sides by 2 to solve for x: x = 1
5. Substitute the value of x into one of the equations to find y and z:

• Using the first equation: 1 + y + 2z = 8
• Simplify: y + 2z = 7
• Using the third equation: 1 - y + 2z = 2
• Simplify: -y + 2z = 1

Combine the two new equations: (y + 2z) + (-y + 2z) = 7 + 1This simplifies to: 4z = 8Divide both sides by 4 to solve for z: z = 2Substitute the values of x and z back into one of the equations to find y:

• Using the first equation: 1 + y + 2(2) = 8
• Simplify: y + 4 = 8
• Subtract 4 from both sides: y = 4

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