Finite Math Examples

$x = 3 y$ , $x + 3 y = 1$

Step 1

Replace all occurrences of $x$ with $3 y$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $x + 3 y = 1$ with $3 y$ .

$(3 y) + 3 y = 1$

$x = 3 y$

Step 1.2

Simplify the left side.

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Step 1.2.1

Add $3 y$ and $3 y$ .

$6 y = 1$

$x = 3 y$

$6 y = 1$

$x = 3 y$

$6 y = 1$

$x = 3 y$

Step 2

Divide each term in $6 y = 1$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 y = 1$ by $6$ .

$\frac{6 y}{6} = \frac{1}{6}$

$x = 3 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{1}{6}$

$x = 3 y$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{6}$

$x = 3 y$

$y = \frac{1}{6}$

$x = 3 y$

$y = \frac{1}{6}$

$x = 3 y$

$y = \frac{1}{6}$

$x = 3 y$

Step 3

Replace all occurrences of $y$ with $\frac{1}{6}$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $x = 3 y$ with $\frac{1}{6}$ .

$x = 3 (\frac{1}{6})$

$y = \frac{1}{6}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Factor $3$ out of $6$ .

$x = 3 (\frac{1}{3 (2)})$

$y = \frac{1}{6}$

Step 3.2.1.2

Cancel the common factor.

$x = 3 (\frac{1}{3 \cdot 2})$

$y = \frac{1}{6}$

Step 3.2.1.3

Rewrite the expression.

$x = \frac{1}{2}$

$y = \frac{1}{6}$

$x = \frac{1}{2}$

$y = \frac{1}{6}$

$x = \frac{1}{2}$

$y = \frac{1}{6}$

$x = \frac{1}{2}$

$y = \frac{1}{6}$

Step 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(\frac{1}{2}, \frac{1}{6})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{1}{2}, \frac{1}{6})$

Equation Form:

$x = \frac{1}{2}, y = \frac{1}{6}$

Step 6