Finite Math Examples

$r - 4 s = 0$ , $5 r - 5 s = 105$

Step 1

Add $4 s$ to both sides of the equation.

$r = 4 s$

$5 r - 5 s = 105$

Step 2

Replace all occurrences of $r$ with $4 s$ in each equation.

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Step 2.1

Replace all occurrences of $r$ in $5 r - 5 s = 105$ with $4 s$ .

$5 (4 s) - 5 s = 105$

$r = 4 s$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $5 (4 s) - 5 s$ .

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Step 2.2.1.1

Multiply $4$ by $5$ .

$20 s - 5 s = 105$

$r = 4 s$

Step 2.2.1.2

Subtract $5 s$ from $20 s$ .

$15 s = 105$

$r = 4 s$

$15 s = 105$

$r = 4 s$

$15 s = 105$

$r = 4 s$

$15 s = 105$

$r = 4 s$

Step 3

Divide each term in $15 s = 105$ by $15$ and simplify.

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Step 3.1

Divide each term in $15 s = 105$ by $15$ .

$\frac{15 s}{15} = \frac{105}{15}$

$r = 4 s$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $15$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{15 s}{15} = \frac{105}{15}$

$r = 4 s$

Step 3.2.1.2

Divide $s$ by $1$ .

$s = \frac{105}{15}$

$r = 4 s$

$s = \frac{105}{15}$

$r = 4 s$

$s = \frac{105}{15}$

$r = 4 s$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $105$ by $15$ .

$s = 7$

$r = 4 s$

$s = 7$

$r = 4 s$

$s = 7$

$r = 4 s$

Step 4

Replace all occurrences of $s$ with $7$ in each equation.

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Step 4.1

Replace all occurrences of $s$ in $r = 4 s$ with $7$ .

$r = 4 (7)$

$s = 7$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4$ by $7$ .

$r = 28$

$s = 7$

$r = 28$

$s = 7$

$r = 28$

$s = 7$

Step 5

List all of the solutions.

$r = 28, s = 7$