Question

How to use the elimination method for the following equations 16x + 12y = 336 11x + 15y = 312

Answer 1

Given the system of equations:

`\begin{gathered} 16x+12y=336\text{ \lparen1\rparen} \\ 11x+15y=312\text{ \lparen2\rparen} \end{gathered}`

The elimination method consists of multiplying either of the two equations in order to have the coefficients of x or y with the same value and be able to add or subtract.

In this case we are going to multiply the equation (2) by 16/11:

`\begin{gathered} (16)/(11)(11x+15y)=(16)/(11)*(312) \\ 16x+(16*15)/(11)y=(16*312)/(11) \\ \\ 16x+(240)/(11)y=(4992)/(11)\text{ \lparen3\rparen} \end{gathered}`

Now, subtracting (1) - (3)

`\begin{gathered} 16x+12y=336 \\ - \\ 16x+(240)/(11)y=(4992)/(11) \end{gathered}`

This is going to be eual to:

`(16x-16x)+(12y-(240)/(11)y)=(336-(4992)/(11))`

Where: 16x-16x=0, therefore:

`12y-(240)/(11)y=336-(4992)/(11)`

Solving for y:

`\begin{gathered} -(108)/(11)y=-(1296)/(11) \\ 108y=1296 \\ y=(1296)/(108)=12 \end{gathered}`

Finally, replacing the value of y in (1) to find x:

`\begin{gathered} 16x+12(12)=336 \\ 16x=336-144 \\ 16x=192 \\ x=(192)/(16)=12 \end{gathered}`

Answer: the solution of the system is x=12, y=12.