Finite Math Examples

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

Step 1

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

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Step 1.1

Subtract $3 y$ from both sides of the equation.

$4 x = 5 - 3 y$

$8 x + 6 y = 8$

Step 1.2

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

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Step 1.2.1

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

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

$8 x + 6 y = 8$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

$8 x + 6 y = 8$

Step 1.2.2.1.2

Divide $x$ by $1$ .

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

$8 x + 6 y = 8$

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

$8 x + 6 y = 8$

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

$8 x + 6 y = 8$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

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

$8 x + 6 y = 8$

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

$8 x + 6 y = 8$

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

$8 x + 6 y = 8$

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

$8 x + 6 y = 8$

Step 2

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

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Step 2.1

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

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $8 (\frac{5}{4} - \frac{3 y}{4}) + 6 y$ .

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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.

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

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

Step 2.2.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.1.2.1

Factor $4$ out of $8$ .

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

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

Step 2.2.1.1.2.2

Cancel the common factor.

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

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

Step 2.2.1.1.2.3

Rewrite the expression.

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

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

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

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

Step 2.2.1.1.3

Multiply $2$ by $5$ .

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

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

Step 2.2.1.1.4

Cancel the common factor of $4$ .

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Step 2.2.1.1.4.1

Move the leading negative in $- \frac{3 y}{4}$ into the numerator.

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

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

Step 2.2.1.1.4.2

Factor $4$ out of $8$ .

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

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

Step 2.2.1.1.4.3

Cancel the common factor.

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

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

Step 2.2.1.1.4.4

Rewrite the expression.

$10 + 2 (- 3 y) + 6 y = 8$

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

$10 + 2 (- 3 y) + 6 y = 8$

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

Step 2.2.1.1.5

Multiply $- 3$ by $2$ .

$10 - 6 y + 6 y = 8$

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

$10 - 6 y + 6 y = 8$

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

Step 2.2.1.2

Combine the opposite terms in $10 - 6 y + 6 y$ .

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Step 2.2.1.2.1

Add $- 6 y$ and $6 y$ .

$10 + 0 = 8$

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

Step 2.2.1.2.2

Add $10$ and $0$ .

$10 = 8$

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

$10 = 8$

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

$10 = 8$

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

$10 = 8$

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

$10 = 8$

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

Step 3

Since $10 = 8$ is not true, there is no solution.

No solution

Step 4