+0

# steps on how to solve?

0
215
1
+569

Aug 14, 2018

#1
+100516
+1

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)

-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)

Aug 14, 2018