Finite Math Examples

$3 x + 2 y = 5$ , $9 x + 6 y = 9$

Step 1

Solve for $x$ in $3 x + 2 y = 5$ .

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Step 1.1

Subtract $2 y$ from both sides of the equation.

$3 x = 5 - 2 y$

$9 x + 6 y = 9$

Step 1.2

Divide each term in $3 x = 5 - 2 y$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 x = 5 - 2 y$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3} + \frac{- 2 y}{3}$

$9 x + 6 y = 9$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3} + \frac{- 2 y}{3}$

$9 x + 6 y = 9$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{3} + \frac{- 2 y}{3}$

$9 x + 6 y = 9$

$x = \frac{5}{3} + \frac{- 2 y}{3}$

$9 x + 6 y = 9$

$x = \frac{5}{3} + \frac{- 2 y}{3}$

$9 x + 6 y = 9$

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.

$x = \frac{5}{3} - \frac{2 y}{3}$

$9 x + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$9 x + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$9 x + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$9 x + 6 y = 9$

Step 2

Replace all occurrences of $x$ with $\frac{5}{3} - \frac{2 y}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $9 x + 6 y = 9$ with $\frac{5}{3} - \frac{2 y}{3}$ .

$9 (\frac{5}{3} - \frac{2 y}{3}) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $9 (\frac{5}{3} - \frac{2 y}{3}) + 6 y$ .

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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.

$9 (\frac{5}{3}) + 9 (- \frac{2 y}{3}) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1

Factor $3$ out of $9$ .

$3 (3) (\frac{5}{3}) + 9 (- \frac{2 y}{3}) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.1.2.2

Cancel the common factor.

$3 \cdot (3 (\frac{5}{3})) + 9 (- \frac{2 y}{3}) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.1.2.3

Rewrite the expression.

$3 \cdot 5 + 9 (- \frac{2 y}{3}) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$3 \cdot 5 + 9 (- \frac{2 y}{3}) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.1.3

Multiply $3$ by $5$ .

$15 + 9 (- \frac{2 y}{3}) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.1.4

Cancel the common factor of $3$ .

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Step 2.2.1.1.4.1

Move the leading negative in $- \frac{2 y}{3}$ into the numerator.

$15 + 9 (\frac{- 2 y}{3}) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.1.4.2

Factor $3$ out of $9$ .

$15 + 3 (3) (\frac{- 2 y}{3}) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.1.4.3

Cancel the common factor.

$15 + 3 \cdot (3 (\frac{- 2 y}{3})) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.1.4.4

Rewrite the expression.

$15 + 3 (- 2 y) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$15 + 3 (- 2 y) + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.1.5

Multiply $- 2$ by $3$ .

$15 - 6 y + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$15 - 6 y + 6 y = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.2

Combine the opposite terms in $15 - 6 y + 6 y$ .

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Step 2.2.1.2.1

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

$15 + 0 = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 2.2.1.2.2

Add $15$ and $0$ .

$15 = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$15 = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$15 = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$15 = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

$15 = 9$

$x = \frac{5}{3} - \frac{2 y}{3}$

Step 3

Since $15 = 9$ is not true, there is no solution.

No solution

Step 4