How do you solve the system x+y-z=2, 3x+5y-2z=-5, and 5x+4y-7z=-7?

1 Answer
Sep 5, 2016

The soln. : x=30, y=-13, z=15.

Explanation:

Let us solve the system of eqns. using Elimination Method.

From the First eqn., z=x+y-2

Using this z in the second and the third eqns., we get,

3x+5y-2(x+y-2)=-5", i.e., "x+3y=-9

5x+4y-7(x+y-2)=-7", or, "-2x-3y=-21

Adding these last eqns., x=30.

Then from, x+3y=-9, y=-13.

Finally, z=x+y-2=15.

These roots satisfy the given eqns.

The soln. : x=30, y=-13, z=15.