Algebra, Trig Solve the system: 7x + 3y = -2, -7x -- 7y =

(7x + 3y) + (-7x -- 7y) = (-2 + 14) 7x + 3y -- 7x -- 7y = 12 -4y = 12 y = -3

Substituting y for the first equation: 7x + 3(-3) = -2 7x -- 9 = -2 7x = 7 x = 1

x = 1, y = -3.

Solve the system: x + y = -5, x -- y = 12

(x + y) + (x -- y) = (-5 + 12) x + y + x -- y = 7 2x = 7 x = 7/2

Substituting x for the first equation: 7/2 + y = -5 y = -5 -- (7/2) y = -17/2

x = 7/2, y = -17/2.

Solve the system: y -- 3z = -12, -2x + y + 2z = 5, 2x + 3z = 7

(y -- 3z) + (-2x + y + 2z) + (2x + 3z) = -12 + 5 + 7 y -- 3z -- 2x + y + 2z + 2x + 3z = 0

2z = 0 y + z = 0 y = -z

Substituting for y for the first equation: -z -- 3z = -12 -4z = -12 z = 3 y = -3

Substituting z for the...

Solve the system: x -- y + z = 6, x + y + z = 2, x + y -- z =0
x + y -- z = 0 x + y = z

Substituting z for the second equation: x + y + 2 = 2 z + z = 2 2z = 2 z = 1

(x -- y + z) + (x + y -- z) = (6 + 0) 2x = 6 x = 3

Substituting x and z for the third equation: 3 + y -- 1 = 0 y + 2 = 0 y = -2

Answer: x = 3, y = -2, z = 1.

6. Solve the system: x -- y + 2z = 7, 2x + z = 4, x + 5y + z = 9

2x + z = 4 z = 4…