Question

Provide a formal check and finishing statementon the following equations:

Answer 1

We have the system of equations:

`\begin{gathered} (x)/(6)+(y)/(4)=6 \\ (5x)/(6)-(y)/(3)=11 \end{gathered}`

We can solve it by elimination: we will multiply the first equation by 5 and substract from the second equation. Then, we will eliminate x and we can solve for y.

We can write this as:

`\begin{gathered} ((5)/(6)x-(1)/(3)y)-5((1)/(6)x+(1)/(4)y)=11-5(6) \\ (5)/(6)x-(1)/(3)y-(5)/(6)x-(5)/(4)y=11-30 \\ 0x-((1)/(3)+(5)/(4))y=-19 \\ -((4+15)/(12))y=-19 \\ (19)/(12)y=19 \\ y=19\cdot(12)/(19) \\ y=12 \end{gathered}`

Now, with the value of y, we can solve for x as:

`\begin{gathered} (1)/(6)x+(1)/(4)y=6 \\ (1)/(6)x+(1)/(4)\cdot12=6 \\ (1)/(6)x+3=6 \\ (1)/(6)x=6-3 \\ (1)/(6)x=3 \\ x=3\cdot6 \\ x=18 \end{gathered}`

Answer: x=18 and y=12