Question

Select the correct answer from each drop-down menu.Consider this system of equations:+y=12 (equation A)y-3x = 6 (equation B)The solution for the system of equations is A.(1118/47, 396/47) B.(33/13, 50/13) C.(99/13, 150/13) D.(8, 12)

Answer 1

Given:

`\begin{gathered} (2)/(3)x+(3)/(5)y=12----(A) \\ \\ (5)/(2)y-3x=6-----(B) \end{gathered}`

Required:

To find the solution of the given equations.

Step-by-step explanation:

Myltiply equation A with 9/2 we get

`3x+(27)/(10)y=54----(C)`

Add equation (C) and (B), we get

`\begin{gathered} (5)/(2)y+(27)/(10)y+60 \\ \\ ((5)/(2)+(27)/(10))y=60 \\ \\ (2.5+2.7)y=60 \\ \\ 5.2y=60 \\ \\ y=(60)/(5.2) \\ \\ y=11.53 \end{gathered}`

Now put y in equation B, we get

`\begin{gathered} (5)/(2)(11.53)-3x=6 \\ \\ 28.825-3x=6 \\ \\ -3x=6-28.825 \\ \\ -3x=-22.825 \\ \\ x=(22.825)/(3) \\ \\ x=7.6 \end{gathered}`

Final Answer:

`((99)/(13),(150)/(13))`