Question

How to solve the following using the elimination method 16x + 12y = 33611x + 15y = 312

Answer 1

Given:

There are given that the two equations:

$\begin{gathered} 16x+12y=336...(1) \\ 11x+15y=312...(2) \end{gathered}$

Explanation:

According to the question:

We need to find the set of the solution by using the elimination method.

So,

From the given equation:

First We need to remove the x term, so we will multiply by 11 in equation (1) ad then we will multiply by 16 in equation (2).

So,

$\begin{gathered} 11\times(16x+12y=336) \\ (11\times16x+11\times12y=11\times336) \\ 176x+132y=3696...(3) \end{gathered}$

Then,

From the equation (2):

$\begin{gathered} 16\times(11x+15y=312) \\ 176x+240y=4992...(4) \end{gathered}$

Now,

We need to subtract equation (3) from equation (4):

Then,

After subtraction, the x term will be called out.

So,

$\begin{gathered} (240-132)y=4992-3696 \\ 108y=1296 \\ y=\frac{1296}{108} \\ y=12 \end{gathered}$

Now,

Put the value of y into equation (1) for getting the value of x.

So,

From the equation (1):

$\begin{gathered} \begin{equation*} 16x+12y=336 \end{equation*} \\ 16x+12(12)=336 \\ 16x+144=336 \\ 16x=336-144 \end{gathered}$

Then,

$\begin{gathered} 16x=336-144 \\ 16x=192 \\ x=\frac{192}{16} \\ x=12 \end{gathered}$

Final answer:

Hence, the solution of the give set of equation is shown below:

$(x,y)=(12,12)$