Finite Math Examples

$2 x \cdot 1 - 2 x \cdot 2 + 5 x \cdot 3 = - 15$ , $4 x \cdot 1 + 20 x \cdot 2 - 54 x \cdot 3 = 74$ , $x \cdot 1 + 3 x \cdot 2 - 8 x \cdot 3 = 10$

Step 1

Divide each term in $13 x = - 15$ by $13$ and simplify.

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Step 1.1

Divide each term in $13 x = - 15$ by $13$ .

$\frac{13 x}{13} = \frac{- 15}{13}$

$- 118 x = 74$

$- 17 x = 10$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $13$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{13 x}{13} = \frac{- 15}{13}$

$- 118 x = 74$

$- 17 x = 10$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 15}{13}$

$- 118 x = 74$

$- 17 x = 10$

$x = \frac{- 15}{13}$

$- 118 x = 74$

$- 17 x = 10$

$x = \frac{- 15}{13}$

$- 118 x = 74$

$- 17 x = 10$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$x = - \frac{15}{13}$

$- 118 x = 74$

$- 17 x = 10$

$x = - \frac{15}{13}$

$- 118 x = 74$

$- 17 x = 10$

$x = - \frac{15}{13}$

$- 118 x = 74$

$- 17 x = 10$

Step 2

Replace all occurrences of $x$ with $- \frac{15}{13}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 118 x = 74$ with $- \frac{15}{13}$ .

$- 118 (- \frac{15}{13}) = 74$

$x = - \frac{15}{13}$

$- 17 x = 10$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $- 118 (- \frac{15}{13})$ .

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Step 2.2.1.1

Multiply $- 1$ by $- 118$ .

$118 (\frac{15}{13}) = 74$

$x = - \frac{15}{13}$

$- 17 x = 10$

Step 2.2.1.2

Combine $118$ and $\frac{15}{13}$ .

$\frac{118 \cdot 15}{13} = 74$

$x = - \frac{15}{13}$

$- 17 x = 10$

Step 2.2.1.3

Multiply $118$ by $15$ .

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

$- 17 x = 10$

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

$- 17 x = 10$

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

$- 17 x = 10$

Step 2.3

Replace all occurrences of $x$ in $- 17 x = 10$ with $- \frac{15}{13}$ .

$- 17 (- \frac{15}{13}) = 10$

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Multiply $- 17 (- \frac{15}{13})$ .

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Step 2.4.1.1

Multiply $- 1$ by $- 17$ .

$17 (\frac{15}{13}) = 10$

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

Step 2.4.1.2

Combine $17$ and $\frac{15}{13}$ .

$\frac{17 \cdot 15}{13} = 10$

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

Step 2.4.1.3

Multiply $17$ by $15$ .

$\frac{255}{13} = 10$

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

$\frac{255}{13} = 10$

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

$\frac{255}{13} = 10$

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

$\frac{255}{13} = 10$

$\frac{1770}{13} = 74$

$x = - \frac{15}{13}$

Step 3

Since $\frac{255}{13} = 10$ is not true, there is no solution.

No solution

Step 4