Finite Math Examples

$2 x \cdot 1 + 3 x \cdot 2 - x \cdot 3 + 3 x \cdot 4 + x \cdot 5 = 176$ , $3 x \cdot 1 + x \cdot 2 - 4 x \cdot 3 + 3 x \cdot 4 - x \cdot 5 = 0$ , $x \cdot 1 + x \cdot 2 + 3 x \cdot 3 - 4 x \cdot 4 + 2 x \cdot 5 = 48$ , $x \cdot 1 + 2 x \cdot 2 - 3 x \cdot 3 + 2 x \cdot 4 - 2 x \cdot 5 = - 48$

Step 1

Divide each term in $22 x = 176$ by $22$ and simplify.

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Step 1.1

Divide each term in $22 x = 176$ by $22$ .

$\frac{22 x}{22} = \frac{176}{22}$

$6 \cdot x = 48$

$- 6 x = - 48$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $22$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{22 x}{22} = \frac{176}{22}$

$6 \cdot x = 48$

$- 6 x = - 48$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{176}{22}$

$6 \cdot x = 48$

$- 6 x = - 48$

$x = \frac{176}{22}$

$6 \cdot x = 48$

$- 6 x = - 48$

$x = \frac{176}{22}$

$6 \cdot x = 48$

$- 6 x = - 48$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $176$ by $22$ .

$x = 8$

$6 \cdot x = 48$

$- 6 x = - 48$

$x = 8$

$6 \cdot x = 48$

$- 6 x = - 48$

$x = 8$

$6 \cdot x = 48$

$- 6 x = - 48$

Step 2

Replace all occurrences of $x$ with $8$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $6 \cdot x = 48$ with $8$ .

$6 \cdot (8) = 48$

$x = 8$

$- 6 x = - 48$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $6$ by $8$ .

$48 = 48$

$x = 8$

$- 6 x = - 48$

$48 = 48$

$x = 8$

$- 6 x = - 48$

Step 2.3

Replace all occurrences of $x$ in $- 6 x = - 48$ with $8$ .

$- 6 \cdot 8 = - 48$

$48 = 48$

$x = 8$

Step 2.4

Simplify the left side.

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Step 2.4.1

Multiply $- 6$ by $8$ .

$- 48 = - 48$

$48 = 48$

$x = 8$

$- 48 = - 48$

$48 = 48$

$x = 8$

$- 48 = - 48$

$48 = 48$

$x = 8$

Step 3

Remove any equations from the system that are always true.

$x = 8$

Step 4