What is the full answer to this problem? (Can you please show work on this so I can see how it is done?)

Question

Solve the following system of equations algebraically.

3x-y=0 

5x+2y=22

Answer 1

3x-y=0                      [eq1]
5x+2y=22                 [eq2]

 

From eq1,

     y = 3x

 

Substitute for y in eq2:

    5x + 2(3x) = 22

      11x = 22

        x = 2

 

Put that into either eq1 or eq2 to solve for y:

     y = 3x

     y = 3(2)

       y = 6

 

Now, checking usually helps find typos and calculation errors (ask any tutor):

 

Does      3x-y=0       ?

             3(2)-6=0    ?

                  0 = 0    ?yes

Does     5x+22y=22    ?

            5(2)+2(6)=22    ?

              10 + 12 = 22    ?

                  22 = 22    ?yes

Answer 2

a) 3x - y = 0

b) 5x + 2y = 22

 

c) 6x - 2y = 0     multiply both sides of a) by 2

d) 5x + 2y = 22  same b)

 

e) 11x = 22          add c) to d)

 

f) x = 2         divide both sides by 8

 

Now substitute 2 for x in any equation and determine value of y.