Solve this system of equations%0D%0A%0D%0Ax+y+z=6%0D%0A%0D%0A+%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A6%0D%0A %0D%0A2x−y+3z=9%0D%0A2%0D%0A%0D%0A−%0D%0A%0D%0A+%0D%0A3%0D%0A%0D%0A=%0D%0A9%0D%0A %0D%0A2x+z=5

Answer 1

To solve the system of equations:

1) x + y + z = 6
2) 2x - y + 3z = 9
3) 2x + z = 5

We can use the method of substitution or elimination. Let's use the method of substitution.

From equation 3, we can express z in terms of x:
z = 5 - 2x

Substitute this expression for z in equation 1:
x + y + (5 - 2x) = 6
-x + y + 5 = 6
-y = -1
y = 1

Now, substitute the values of y and z in equation 2:
2x - 1 + 3(5 - 2x) = 9
2x - 1 + 15 - 6x = 9
-4x + 14 = 9
-4x = -5
x = 5/4 or 1.25

Finally, substitute the values of x and y in equation 1 to find z:
1.25 + 1 + z = 6
z = 6 - 2.25
z = 3.75

Therefore, the solution to the system of equations is x = 1.25, y = 1, and z = 3.75.