Finite Math Examples

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

Step 1

Divide each term in $16 x = 5$ by $16$ and simplify.

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Step 1.1

Divide each term in $16 x = 5$ by $16$ .

$\frac{16 x}{16} = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $16$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{16 x}{16} = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

$x = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

$x = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

$x = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

Step 2

Replace all occurrences of $x$ with $\frac{5}{16}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 27 x = - 3$ with $\frac{5}{16}$ .

$- 27 (\frac{5}{16}) = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 27 (\frac{5}{16})$ .

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Step 2.2.1.1

Multiply $- 27 (\frac{5}{16})$ .

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Step 2.2.1.1.1

Combine $- 27$ and $\frac{5}{16}$ .

$\frac{- 27 \cdot 5}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

Step 2.2.1.1.2

Multiply $- 27$ by $5$ .

$\frac{- 135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

$\frac{- 135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

Step 2.2.1.2

Move the negative in front of the fraction.

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

Step 2.3

Replace all occurrences of $x$ in $- 5 x = 1$ with $\frac{5}{16}$ .

$- 5 (\frac{5}{16}) = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $- 5 (\frac{5}{16})$ .

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Step 2.4.1.1

Multiply $- 5 (\frac{5}{16})$ .

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Step 2.4.1.1.1

Combine $- 5$ and $\frac{5}{16}$ .

$\frac{- 5 \cdot 5}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

Step 2.4.1.1.2

Multiply $- 5$ by $5$ .

$\frac{- 25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$\frac{- 25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

Step 2.4.1.2

Move the negative in front of the fraction.

$- \frac{25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- \frac{25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- \frac{25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- \frac{25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

Step 3

Since $- \frac{25}{16} = 1$ is not true, there is no solution.

No solution

Step 4