78x+91y=39 and 65x+117y=42 solve the equation by elimination method
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What is the elimination method?
The elimination method is a technique for solving systems of linear equations. Let's walk through a couple of examples.
Example 1
We're asked to solve this system of equations:
\begin{aligned} 2y+7x &= -5\\\\ 5y-7x &= 12 \end{aligned}2y+7x5y−7x=−5=12
We notice that the first equation has a 7x7x7, xterm and the second equation has a -7x−7xminus, 7, xterm. These terms will cancel if we add the equations together—that is, we'll eliminate the xxx terms:
2y+7x+ 5y−7x7y+0=−5=12=7
Solving for yyy, we get:
\begin{aligned} 7y+0 &=7\\\\ 7y &=7\\\\ y &=\goldD{1} \end{aligned}7y+07yy=7=7=1
The elimination method is a technique for solving systems of linear equations. Let's walk through a couple of examples.
Example 1
We're asked to solve this system of equations:
\begin{aligned} 2y+7x &= -5\\\\ 5y-7x &= 12 \end{aligned}2y+7x5y−7x=−5=12
We notice that the first equation has a 7x7x7, xterm and the second equation has a -7x−7xminus, 7, xterm. These terms will cancel if we add the equations together—that is, we'll eliminate the xxx terms:
2y+7x+ 5y−7x7y+0=−5=12=7
Solving for yyy, we get:
\begin{aligned} 7y+0 &=7\\\\ 7y &=7\\\\ y &=\goldD{1} \end{aligned}7y+07yy=7=7=1
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