What is the solution for the system of equations

Question

Write answering x,y form

2y=3x-5

8x+16=20y

Answer 1

2y=3x-5

8x+16=20y

 

y=(3x-5)/2

 

8x+16=20((3x-5)/2)

8x+16=10(3x-5)

8x+16=30x-50

22x=66

x=3

 

y=(3(3)-5)/2

y=2

 

(3,2)

Answer 2

Write answering x,y form
2y=3x-5

multipy the above by 10

20y=30x-50
8x+16=20y

 

eliminate y

30x-50=8x+16

22x=66

x=3

from

2y=3x-5

2y=3(3)-5=4

y=2

 

check

 

8x+16=20y

8(3)+16=20(2)

40=40

 

Checks out

 

solution is (3,2)

Answer 3

First put the equations in standard form Ax + By = C

 

-3x + 2y = -5

 8x - 20y = -16

 

Multiply the 1st equation by 10 and then add the 2 equations together 

 

-30x + 20y = -50

   8x  - 20y = -16

 

-22x = -66

x = 3

 

Plug this value of x in to the original 1st equation 

 

2y = 3(3) - 5 = 4

y = 2

 

So x = 3 and y = 2 

 

Check:  2(2) = 4, 3(3) - 5 = 4 

            8(3) + 16 = 40, 20(2) = 40