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Solve the system of equations: 3x + 4y = 33 y = 2 - 4 11 Fill in the coordinates of the ordered pair:(

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The system of equations we have is:


\begin{gathered} \\ \mleft\{\begin{aligned}3x+4y=33 \\ y=x-4\end{aligned}\mright. \end{gathered}

To solve it, we need to have the variables of both equations on the same side.

Step 1: Substract x from both sides of the second equation


\begin{gathered} y-x=x-x-4 \\ y-x=-4 \\ -x+y=-4 \end{gathered}

And now the system is:


\{\begin{aligned}3x+4y=33 \\ -x+y=-4\end{aligned}

Step 2: We need to eliminate one variable to solve, for this reason now we multiply the second equation by 3


\begin{gathered} 3(-x+y=-4) \\ -3x+3y=-12 \end{gathered}

And we add this with the first equation of the system


\begin{gathered} 3x+4y=33 \\ -3x+3y=-12 \\ ----------- \\ 0x+7y=21 \end{gathered}

which is the same as:


7y=21

Step 3: solve this previous equation for y, by dividing both sides by 7


\begin{gathered} (7y)/(7)=(21)/(7) \\ y=3 \end{gathered}

Step 4: with the value for y, we find the value of x.

Substituting y=3 in the second equation of the original system of equations:


y=x-4
3=x-4

We add 4 to both sides:


\begin{gathered} 3+4=x \\ 7=x \end{gathered}

Answer: y=3 and x=7, representing the result as an ordered pair: (7, 3)

User SLLegendre
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