Remember that the steps to solve a system of linear equations (2x2) are:
0. Arrange the equations with like terms in columns.
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1. Analyze the coefficients of x or y, and try to eliminate one.
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2. Add the equations and solve for the remaining variable.
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3. Substitute the value into either equation and solve.
Notice that if we multiply equation 1 by -2 and add it up with equation 2, we'll eliminate x , as following:
[tex]\begin{gathered} \begin{cases}2x-y=2 \\ 4x+3y=24\end{cases}\rightarrow\begin{cases}-4x+2y=-4 \\ 4x+3y=24\end{cases} \\ \\ \rightarrow5y=20\rightarrow y=\frac{20}{5}\Rightarrow y=4 \end{gathered}[/tex]
Now, we plug in this value in equation 2 and solve for x :
[tex]\begin{gathered} 4x+3y=24\rightarrow4x+3(4)=24\rightarrow4x+12=24 \\ \rightarrow4x=12\rightarrow x=\frac{12}{4}\Rightarrow x=3 \end{gathered}[/tex]
