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:

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

Required:

To find the solution of the given equations.

Explanation:

Myltiply equation A with 9/2 we get

$3x+\frac{27}{10}y=54----(C)$

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

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

Now put y in equation B, we get

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

Final Answer:

$(\frac{99}{13},\frac{150}{13})$