Finite Math Examples

$8 x - 7 y = 3$ , $16 x - 14 y = 6$

Step 1

Solve for $x$ in $8 x - 7 y = 3$ .

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Step 1.1

Add $7 y$ to both sides of the equation.

$8 x = 3 + 7 y$

$16 x - 14 y = 6$

Step 1.2

Divide each term in $8 x = 3 + 7 y$ by $8$ and simplify.

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Step 1.2.1

Divide each term in $8 x = 3 + 7 y$ by $8$ .

$\frac{8 x}{8} = \frac{3}{8} + \frac{7 y}{8}$

$16 x - 14 y = 6$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{3}{8} + \frac{7 y}{8}$

$16 x - 14 y = 6$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{8} + \frac{7 y}{8}$

$16 x - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$16 x - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$16 x - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$16 x - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$16 x - 14 y = 6$

Step 2

Replace all occurrences of $x$ with $\frac{3}{8} + \frac{7 y}{8}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $16 x - 14 y = 6$ with $\frac{3}{8} + \frac{7 y}{8}$ .

$16 (\frac{3}{8} + \frac{7 y}{8}) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $16 (\frac{3}{8} + \frac{7 y}{8}) - 14 y$ .

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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.

$16 (\frac{3}{8}) + 16 (\frac{7 y}{8}) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.1.2

Cancel the common factor of $8$ .

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Step 2.2.1.1.2.1

Factor $8$ out of $16$ .

$8 (2) (\frac{3}{8}) + 16 (\frac{7 y}{8}) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.1.2.2

Cancel the common factor.

$8 \cdot (2 (\frac{3}{8})) + 16 (\frac{7 y}{8}) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.1.2.3

Rewrite the expression.

$2 \cdot 3 + 16 (\frac{7 y}{8}) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$2 \cdot 3 + 16 (\frac{7 y}{8}) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.1.3

Multiply $2$ by $3$ .

$6 + 16 (\frac{7 y}{8}) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.1.4

Cancel the common factor of $8$ .

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Step 2.2.1.1.4.1

Factor $8$ out of $16$ .

$6 + 8 (2) (\frac{7 y}{8}) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.1.4.2

Cancel the common factor.

$6 + 8 \cdot (2 (\frac{7 y}{8})) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.1.4.3

Rewrite the expression.

$6 + 2 (7 y) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$6 + 2 (7 y) - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.1.5

Multiply $7$ by $2$ .

$6 + 14 y - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$6 + 14 y - 14 y = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.2

Combine the opposite terms in $6 + 14 y - 14 y$ .

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Step 2.2.1.2.1

Subtract $14 y$ from $14 y$ .

$6 + 0 = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 2.2.1.2.2

Add $6$ and $0$ .

$6 = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$6 = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$6 = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$6 = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

$6 = 6$

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{3}{8} + \frac{7 y}{8}$

Step 4