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4x + 8y = 4 and -2x - 7y = -11

4x + 8y = 4 and -2x - 7y = -11-example-1

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We have the following system of equations:


\begin{gathered} 4x+8y=4 \\ -2x-7y=-11\ldots(A) \end{gathered}

Solving by combining equations:

If we multiply equation A by 2, we get the following equivalent system:


\begin{gathered} \\ 4x+8y=4\ldots(B) \\ -4x-14y=-22\ldots(C) \end{gathered}

If we add both equation, we have


8y-14y=4-22

which gives


-6y=-18

If we move the coefficient of y, we get


\begin{gathered} y=(-18)/(-6) \\ y=3 \end{gathered}

Finally, by substituting this result into equation B, we obtain


4x+8(3)=4

which leads to


4x+24=4

If we move +24 to the right hand side,we get


\begin{gathered} 4x=4-24 \\ 4x=-20 \end{gathered}

and x is given by


\begin{gathered} x=(-20)/(4) \\ x=-5 \end{gathered}

Therefore, the answer is


\begin{gathered} x=-5 \\ y=3 \end{gathered}

User Sakthisundar
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