Question

Solve the following system of three equations:

2x+3y−z = 5
4x−2y+3z = 12
x+y+2z = -3

Answer 1

To solve the system of equations, multiply and add the equations to eliminate variables, and then substitute the values back into the original equations to find the solutions for x, y, and z.

Step-by-step explanation:

To solve the system of equations:

2x + 3y - z = 5

4x - 2y + 3z = 12

2x + y + 2z = -3

1. Multiply the first equation by 2 and subtract the third equation from it to eliminate x. This gives us -4y - 4z = -13.
2. Multiply the second equation by 3 and add the first equation to eliminate y. This gives us 14x + 7z = 48.
3. Add the new equations obtained in steps 1 and 2 to eliminate z. This gives us 14x = 35, so x = 35/14 = 5/2 = 2.5.
4. Substitute the value of x into the second equation to solve for y. This gives us 4(2.5) - 2y + 3z = 12, which simplifies to -2y + 3z = 2.
5. Substitute the values of x and y into the first equation to solve for z. This gives us 2(2.5) + 3(2) - z = 5, which simplifies to 8.5 - z = 5, so z = 8.5 - 5 = 3.5.

Therefore, the solution to the system of equations is x = 2.5, y = -1, and z = 3.5.