x-2y=10 1/2x-2y=4

Question

x-2y=10

1/2x-2y=4

please help and show step by step instructions

Answer 1

    x     -2y=10
1/2x    -2y=4

subtract the second equation from the first to get

1/2 x=6 or x=12

substitute in first equation to get 12-2y=10  or 12-2 =10 so 2y=2  y=1

Answer 2

First solve for x in the first equation:  x-2y=10        (a)  Add +2y to each side  x-2y + 2y=10 + 2y

                                                 (b)  -2y plus 2y = 0, so you are left with   x=10+2y

Next plug x= 10+2y into the next equation of 1/2x-2y=4

(a)  1/2(10+2y)-2y=4  Solve for y:  1/2(10) + 1/2(2y)-2y=4

                                                     5+y-2y=4

                                                     5-y=4

                                                      Add +y to each side  5-y+y= 4+y

                                                       5=4+y  then subtract 4 from each side

                                                   5-4=4-4+y  then 1=y

Now plug y into the x=10+2y which is x=10+2(1)=12, so x=12 and y=1

You can check if this is correct by plugging the numbers into either equation.

 

Hope this helps!

 

Kathleen F.

 

 

 

Answer 3

Hi James!

There's a common element to both equations ==> the "2y" ...

swap the "2y's" with "10" and "4" ... x-10=2y, (1/2)x-4=2y ... both recipes = 2y

leaving x-10=(1/2)x-4 ... x-(1/2)x= -4+10 ... (1/2)x=6 ==> x=12, y=1: 12-2(1)=10

STRATEGY: isolate the common element and equate ... Best regards, sir :)