Question

Solve the eq for the values of x, y and z when x+2y+z=7 x+3z=11 and 2x-3y=1​

Answer 1

Lets number the two equations:

Eq 1: 3x + y - 3z = 11

Eq 2: 2x + 5y - 2z = 29

I've swapped the y and z terms in eq 2.

Multiply Eq 1 by a factor 2 and eq 2 by a factor of 3:

6x + 2y - 6z = 22

6x + 15y - 6z = 87

Subtract Eq 1 from eq 2:

6x + 15y - 6z - (6x + 2y - 6z) = 87 - 22

or

6x - 6x + 15y - 2y - 6z + 6z = 65

or

13y = 65 and therefore y = 5

Look at eq1: We can rewrite this as 3(x - z) + y = 11

We know y = 5 and there fore eq 1 can be rewritten as 3(x - z) + 5 = 11

or (x - z) = (11 - 5)/3 = 2

So lets add up (x - z) and y:

(x - z) + y = 2 + 5

or x + y - z = 7