+129852 3x + y = 4 (1)
2x + y = 7 multiply this through by -1 ⇒ -2x - y = -7 (2)
Add (1) and (2) ⇒ x = -3
Subbing into either equation to find y we get 3 (-3) + y = 4 ⇒ -9 + y = 4 add 9 to both sides y = 13
(-3, 13) is the solution
-2x + 6y = -38 multiply through by 3 ⇒ -6x + 18y = -114 (1)
3x - 4y = 32 multiply through by 2 ⇒ 6x - 8y = 64 (2)
Add (1) and (2) ⇒ 10y = -50 ⇒ divide through by 10 ⇒ y = - 5
Subbing this back into the first equation to find x, we get -2x + 6(-5) = -38
-2x - 30 = -38
Add 30 to both sides -2x = -8
Divide both sides by -2
x = 4
(4, -5) is the solution
Last one
x + 3y - z = 6 (1)
4x - 2y + 2z = -10 divide through by 2 ⇒ 2x - y + z = -5 (2)
6x + z = -12 ⇒ z = -12 - 6x (3)
Sub (3) into (1) and (2) for z
x + 3y - [ -12 - 6x] = 6 ⇒ x + 3y + 12 + 6x = 6 ⇒ 7x + 3y = -6 (4)
2x - y + [ -12 - 6x] = -5 ⇒ 2x - y - 12 - 6x = -5 ⇒ -4x - y = 7 mulltiply through by 3 ⇒
-12x - 3y = 21 ( 5)
Add (4) and (5)
-5x = 15 divide through by -5
x = -3
Using (4) we can find y ⇒ 7(-3) + 3y = -6 ⇒ -21 + 3y = -6 ⇒ 3y = 15 ⇒ y = 5
Using (3) we can find z ⇒ z = -12 -6(-3) ⇒ z = -12 + 18 ⇒ z = 6
So...the solution is (-3, 5, 6)
