Finite Math Examples

$x - \frac{1}{6} y = 1$ , $\frac{6}{7} x - \frac{1}{7} y = 1$

Step 1

Solve for $x$ in $x - \frac{1}{6} y = 1$ .

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Step 1.1

Combine $y$ and $\frac{1}{6}$ .

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

$\frac{6}{7} x - \frac{1}{7} y = 1$

Step 1.2

Add $\frac{y}{6}$ to both sides of the equation.

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

$\frac{6}{7} x - \frac{1}{7} y = 1$

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

$\frac{6}{7} x - \frac{1}{7} y = 1$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $\frac{6}{7} x - \frac{1}{7} y = 1$ with $1 + \frac{y}{6}$ .

$\frac{6}{7} \cdot (1 + \frac{y}{6}) - \frac{1}{7} y = 1$

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $\frac{6}{7} \cdot (1 + \frac{y}{6}) - \frac{1}{7} y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$\frac{6}{7} \cdot 1 + \frac{6}{7} \cdot \frac{y}{6} - \frac{1}{7} y = 1$

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

Step 2.2.1.1.2

Multiply $\frac{6}{7}$ by $1$ .

$\frac{6}{7} + \frac{6}{7} \cdot \frac{y}{6} - \frac{1}{7} y = 1$

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

Step 2.2.1.1.3

Cancel the common factor of $6$ .

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Step 2.2.1.1.3.1

Cancel the common factor.

$\frac{6}{7} + \frac{6}{7} \cdot \frac{y}{6} - \frac{1}{7} y = 1$

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

Step 2.2.1.1.3.2

Rewrite the expression.

$\frac{6}{7} + \frac{1}{7} y - \frac{1}{7} y = 1$

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

$\frac{6}{7} + \frac{1}{7} y - \frac{1}{7} y = 1$

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

Step 2.2.1.1.4

Combine $\frac{1}{7}$ and $y$ .

$\frac{6}{7} + \frac{y}{7} - \frac{1}{7} y = 1$

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

Step 2.2.1.1.5

Combine $y$ and $\frac{1}{7}$ .

$\frac{6}{7} + \frac{y}{7} - \frac{y}{7} = 1$

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

$\frac{6}{7} + \frac{y}{7} - \frac{y}{7} = 1$

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

Step 2.2.1.2

Combine the opposite terms in $\frac{6}{7} + \frac{y}{7} - \frac{y}{7}$ .

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Step 2.2.1.2.1

Subtract $\frac{y}{7}$ from $\frac{y}{7}$ .

$\frac{6}{7} + 0 = 1$

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

Step 2.2.1.2.2

Add $\frac{6}{7}$ and $0$ .

$\frac{6}{7} = 1$

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

$\frac{6}{7} = 1$

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

$\frac{6}{7} = 1$

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

$\frac{6}{7} = 1$

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

$\frac{6}{7} = 1$

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

Step 3

Since $\frac{6}{7} = 1$ is not true, there is no solution.

No solution

Step 4