Finite Math Examples

$3 = 5 x - 4 y$ , $- 6 = - 10 x + 8 y$

Step 1

Solve for $x$ in $3 = 5 x - 4 y$ .

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Step 1.1

Rewrite the equation as $5 x - 4 y = 3$ .

$5 x - 4 y = 3$

$- 6 = - 10 x + 8 y$

Step 1.2

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

$5 x = 3 + 4 y$

$- 6 = - 10 x + 8 y$

Step 1.3

Divide each term in $5 x = 3 + 4 y$ by $5$ and simplify.

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Step 1.3.1

Divide each term in $5 x = 3 + 4 y$ by $5$ .

$\frac{5 x}{5} = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 10 x + 8 y$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 10 x + 8 y$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 10 x + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 10 x + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 10 x + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 10 x + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 10 x + 8 y$

Step 2

Replace all occurrences of $x$ with $\frac{3}{5} + \frac{4 y}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 6 = - 10 x + 8 y$ with $\frac{3}{5} + \frac{4 y}{5}$ .

$- 6 = - 10 (\frac{3}{5} + \frac{4 y}{5}) + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- 10 (\frac{3}{5} + \frac{4 y}{5}) + 8 y$ .

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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.

$- 6 = - 10 (\frac{3}{5}) - 10 \frac{4 y}{5} + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.1.2

Cancel the common factor of $5$ .

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Step 2.2.1.1.2.1

Factor $5$ out of $- 10$ .

$- 6 = 5 (- 2) (\frac{3}{5}) - 10 \frac{4 y}{5} + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.1.2.2

Cancel the common factor.

$- 6 = 5 \cdot (- 2 (\frac{3}{5})) - 10 \frac{4 y}{5} + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.1.2.3

Rewrite the expression.

$- 6 = - 2 \cdot 3 - 10 \frac{4 y}{5} + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 2 \cdot 3 - 10 \frac{4 y}{5} + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.1.3

Multiply $- 2$ by $3$ .

$- 6 = - 6 - 10 \frac{4 y}{5} + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.1.4

Cancel the common factor of $5$ .

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Step 2.2.1.1.4.1

Factor $5$ out of $- 10$ .

$- 6 = - 6 + 5 (- 2) (\frac{4 y}{5}) + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.1.4.2

Cancel the common factor.

$- 6 = - 6 + 5 \cdot (- 2 \frac{4 y}{5}) + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.1.4.3

Rewrite the expression.

$- 6 = - 6 - 2 (4 y) + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 6 - 2 (4 y) + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.1.5

Multiply $4$ by $- 2$ .

$- 6 = - 6 - 8 y + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 6 - 8 y + 8 y$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.2

Combine the opposite terms in $- 6 - 8 y + 8 y$ .

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Step 2.2.1.2.1

Add $- 8 y$ and $8 y$ .

$- 6 = - 6 + 0$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 2.2.1.2.2

Add $- 6$ and $0$ .

$- 6 = - 6$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 6$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 6$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 6$

$x = \frac{3}{5} + \frac{4 y}{5}$

$- 6 = - 6$

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{3}{5} + \frac{4 y}{5}$

Step 4