1 Answer

Keydon · Answer 1 · 2023-02-27T14:20:54+0000

Given:

There are given that the two equations:

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

Step-by-step 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,

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

Then,

From the equation (2):

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

Now,

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

Then,

After subtraction, the x term will be called out.

So,

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

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,

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

Final answer:

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

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