Finite Math Examples

$5 x \cdot 1 + 17 x \cdot 2 + 4 x \cdot 3 = 12$ , $2 x \cdot 1 + 7 x \cdot 2 + 4 x \cdot 3 = - 5$ , $x \cdot 1 + 3 x \cdot 2 - 4 x \cdot 3 = 4$

Step 1

Divide each term in $51 x = 12$ by $51$ and simplify.

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Step 1.1

Divide each term in $51 x = 12$ by $51$ .

$\frac{51 x}{51} = \frac{12}{51}$

$28 x = - 5$

$- 5 x = 4$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $51$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{51 x}{51} = \frac{12}{51}$

$28 x = - 5$

$- 5 x = 4$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{51}$

$28 x = - 5$

$- 5 x = 4$

$x = \frac{12}{51}$

$28 x = - 5$

$- 5 x = 4$

$x = \frac{12}{51}$

$28 x = - 5$

$- 5 x = 4$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $12$ and $51$ .

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Step 1.3.1.1

Factor $3$ out of $12$ .

$x = \frac{3 (4)}{51}$

$28 x = - 5$

$- 5 x = 4$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $3$ out of $51$ .

$x = \frac{3 \cdot 4}{3 \cdot 17}$

$28 x = - 5$

$- 5 x = 4$

Step 1.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 4}{3 \cdot 17}$

$28 x = - 5$

$- 5 x = 4$

Step 1.3.1.2.3

Rewrite the expression.

$x = \frac{4}{17}$

$28 x = - 5$

$- 5 x = 4$

$x = \frac{4}{17}$

$28 x = - 5$

$- 5 x = 4$

$x = \frac{4}{17}$

$28 x = - 5$

$- 5 x = 4$

$x = \frac{4}{17}$

$28 x = - 5$

$- 5 x = 4$

$x = \frac{4}{17}$

$28 x = - 5$

$- 5 x = 4$

Step 2

Replace all occurrences of $x$ with $\frac{4}{17}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $28 x = - 5$ with $\frac{4}{17}$ .

$28 (\frac{4}{17}) = - 5$

$x = \frac{4}{17}$

$- 5 x = 4$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $28 (\frac{4}{17})$ .

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Step 2.2.1.1

Combine $28$ and $\frac{4}{17}$ .

$\frac{28 \cdot 4}{17} = - 5$

$x = \frac{4}{17}$

$- 5 x = 4$

Step 2.2.1.2

Multiply $28$ by $4$ .

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

$- 5 x = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

$- 5 x = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

$- 5 x = 4$

Step 2.3

Replace all occurrences of $x$ in $- 5 x = 4$ with $\frac{4}{17}$ .

$- 5 (\frac{4}{17}) = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $- 5 (\frac{4}{17})$ .

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Step 2.4.1.1

Multiply $- 5 (\frac{4}{17})$ .

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Step 2.4.1.1.1

Combine $- 5$ and $\frac{4}{17}$ .

$\frac{- 5 \cdot 4}{17} = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

Step 2.4.1.1.2

Multiply $- 5$ by $4$ .

$\frac{- 20}{17} = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

$\frac{- 20}{17} = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

Step 2.4.1.2

Move the negative in front of the fraction.

$- \frac{20}{17} = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

$- \frac{20}{17} = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

$- \frac{20}{17} = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

$- \frac{20}{17} = 4$

$\frac{112}{17} = - 5$

$x = \frac{4}{17}$

Step 3

Since $- \frac{20}{17} = 4$ is not true, there is no solution.

No solution

Step 4