Finite Math Examples

$x + y = 6$ , $x = \frac{y}{2}$ , $y = \frac{x}{2}$ , $850 x + 440 y = 4000$ , $x = 0$ , $y = 0$

Step 1

Replace all occurrences of $x$ with $0$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $x + y = 6$ with $0$ .

$(0) + y = 6$

$x = 0$

$x = \frac{y}{2}$

$y = \frac{x}{2}$

$850 x + 440 y = 4000$

$y = 0$

Step 1.2

Simplify the left side.

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Step 1.2.1

Add $0$ and $y$ .

$y = 6$

$x = 0$

$x = \frac{y}{2}$

$y = \frac{x}{2}$

$850 x + 440 y = 4000$

$y = 0$

$y = 6$

$x = 0$

$x = \frac{y}{2}$

$y = \frac{x}{2}$

$850 x + 440 y = 4000$

$y = 0$

Step 1.3

Replace all occurrences of $x$ in $x = \frac{y}{2}$ with $0$ .

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = \frac{x}{2}$

$850 x + 440 y = 4000$

$y = 0$

Step 1.4

Simplify the left side.

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Step 1.4.1

Remove parentheses.

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = \frac{x}{2}$

$850 x + 440 y = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = \frac{x}{2}$

$850 x + 440 y = 4000$

$y = 0$

Step 1.5

Replace all occurrences of $x$ in $y = \frac{x}{2}$ with $0$ .

$y = \frac{0}{2}$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$850 x + 440 y = 4000$

$y = 0$

Step 1.6

Simplify the right side.

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Step 1.6.1

Divide $0$ by $2$ .

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$850 x + 440 y = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$850 x + 440 y = 4000$

$y = 0$

Step 1.7

Replace all occurrences of $x$ in $850 x + 440 y = 4000$ with $0$ .

$850 (0) + 440 y = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = 0$

Step 1.8

Simplify the left side.

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Step 1.8.1

Simplify $850 (0) + 440 y$ .

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Step 1.8.1.1

Multiply $850$ by $0$ .

$0 + 440 y = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = 0$

Step 1.8.1.2

Add $0$ and $440 y$ .

$440 y = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = 0$

$440 y = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = 0$

$440 y = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = 0$

$440 y = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = 0$

Step 2

Replace all occurrences of $y$ with $0$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $440 y = 4000$ with $0$ .

$440 (0) = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = 0$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $440$ by $0$ .

$0 = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = 0$

$0 = 4000$

$y = 0$

$0 = \frac{y}{2}$

$y = 6$

$x = 0$

$y = 0$

Step 2.3

Replace all occurrences of $y$ in $0 = \frac{y}{2}$ with $0$ .

$0 = \frac{0}{2}$

$0 = 4000$

$y = 0$

$y = 6$

$x = 0$

$y = 0$

Step 2.4

Simplify the right side.

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Step 2.4.1

Divide $0$ by $2$ .

$0 = 0$

$0 = 4000$

$y = 0$

$y = 6$

$x = 0$

$y = 0$

$0 = 0$

$0 = 4000$

$y = 0$

$y = 6$

$x = 0$

$y = 0$

$0 = 0$

$0 = 4000$

$y = 0$

$y = 6$

$x = 0$

$y = 0$

Step 3

Since $0 = 4000$ is not true, there is no solution.

No solution

Step 4