Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x, y, and z in terms of the parameter a.)

Question

3x-3y+6z=15
x+2y-z=11
5x-8y+13z=19

Answer 1

Eq1: 3x-3y+6z = 15
Eq2:-3x-6y+3z = -3(times-3).
sum: =9y+9z = -18, y + z = -2.

Eq2: -5x-10y+5z = -55(times-5).
Eq3: +5x-8y+13z = 19
Sum: -18y+18z =-36, y - z = 2.

y + z = -2.
y - z = +2.
Sum: 2y = 0, y = 0. z = -2.

Eq1: 3x-3y+6z = 15.
3x - 3*0 + 6(-2) = 15,
3x = 27, x = 9.

Solution: (x, y, z) = (9,0,-2).

To check your solutions, plug the values of x, y, and z into the given Eqs.