1.) Solve this system of linear equations. Write the final answer as an ordered pair (x, y, -3).

Question

x - y + 2z = 22
3y - 8z = -9
z = -3

2.) Solve this system of linear equations. Write the final answer as an ordered pair (x, y, z).

2x + 4y + z = 1
x - 2y - 3z = 2
x + y - z = -1

Answer 1

using substitution,
z = -3, so
3y-8(-3) = -9
3y = -33
y = -11
so,
x-(-11)+2(-3) = 22
x+11-6 = 22
x = 17
So the solution is (17,-11,-3)

The other is not quite so simple, but

since z = 1-2x-4y, we have
x-2y-3(1-2x-4y) = 2
x+y-(1-2x-4y) = -1
or,
7x+10y = 5
3x+5y = 0
So, since 5y = -3x, 10y = -6x and we have
7x-6x = 5
x = 5
so, y = -3
and z = 3

solution is (5,-3,3)