Algebra Examples

$m = 5 n - 3$ $m = 3 n + 7$

Step 1

Eliminate the equal sides of each equation and combine.

$5 n - 3 = 3 n + 7$

Step 2

Solve $5 n - 3 = 3 n + 7$ for $n$ .

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Step 2.1

Move all terms containing $n$ to the left side of the equation.

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Step 2.1.1

Subtract $3 n$ from both sides of the equation.

$5 n - 3 - 3 n = 7$

Step 2.1.2

Subtract $3 n$ from $5 n$ .

$2 n - 3 = 7$

Step 2.2

Move all terms not containing $n$ to the right side of the equation.

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Step 2.2.1

Add $3$ to both sides of the equation.

$2 n = 7 + 3$

Step 2.2.2

Add $7$ and $3$ .

$2 n = 10$

Step 2.3

Divide each term in $2 n = 10$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 n = 10$ by $2$ .

$\frac{2 n}{2} = \frac{10}{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 n}{2} = \frac{10}{2}$

Step 2.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{10}{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $10$ by $2$ .

$n = 5$

Step 3

The solution of the system of equations is all the values that make the system true.

$n = 5$