\[\begin{aligned}&3x+4y=37\\&3x-2y=13\end{aligned}\]

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Examples

Available Methods

Substitution

Elimination

Matrix

Solve for

x

3x+4y=37

Solve for

x

3x+4y=37

Subtract

4y

from both sides.

3x=37-4y

Divide both sides by

3

x=\frac{37-4y}{3}

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x=\frac{37-4y}{3}

Substitute

x=\frac{37-4y}{3}

into

3x-2y=13

Start with the original equation.

3x-2y=13

Let

x=\frac{37-4y}{3}

3\times \frac{37-4y}{3}-2y=13

Simplify.

37-6y=13

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37-6y=13

Solve for

y

37-6y=13

Solve for

y

37-6y=13

Subtract

37

from both sides.

-6y=13-37

Simplify

13-37

-24

-6y=-24

Divide both sides by

-6

y=\frac{-24}{-6}

Two negatives make a positive.

y=\frac{24}{6}

Simplify

\frac{24}{6}

4

y=4

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y=4

Substitute

y=4

into

x=\frac{37-4y}{3}

Start with the original equation.

x=\frac{37-4y}{3}

Let

y=4

x=\frac{37-4\times 4}{3}

Simplify.

x=7

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x=7

Therefore,

\begin{aligned}&x=7\\&y=4\end{aligned}

Done

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