Finite Math Examples

$x - y = 8$ , $x + y = 20$ , $- 3 x + y = 12$ , $x = 0$ , $y = 0$

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 $x - y = 8$ with $0$ .

$(0) - y = 8$

$x = 0$

$x + y = 20$

$- 3 x + y = 12$

$y = 0$

Step 1.2

Simplify the left side.

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Step 1.2.1

Subtract $y$ from $0$ .

$- y = 8$

$x = 0$

$x + y = 20$

$- 3 x + y = 12$

$y = 0$

$- y = 8$

$x = 0$

$x + y = 20$

$- 3 x + y = 12$

$y = 0$

Step 1.3

Replace all occurrences of $x$ in $x + y = 20$ with $0$ .

$(0) + y = 20$

$- y = 8$

$x = 0$

$- 3 x + y = 12$

$y = 0$

Step 1.4

Simplify the left side.

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Step 1.4.1

Add $0$ and $y$ .

$y = 20$

$- y = 8$

$x = 0$

$- 3 x + y = 12$

$y = 0$

$y = 20$

$- y = 8$

$x = 0$

$- 3 x + y = 12$

$y = 0$

Step 1.5

Replace all occurrences of $x$ in $- 3 x + y = 12$ with $0$ .

$- 3 \cdot 0 + y = 12$

$y = 20$

$- y = 8$

$x = 0$

$y = 0$

Step 1.6

Simplify the left side.

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Step 1.6.1

Simplify $- 3 \cdot 0 + y$ .

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Step 1.6.1.1

Multiply $- 3$ by $0$ .

$0 + y = 12$

$y = 20$

$- y = 8$

$x = 0$

$y = 0$

Step 1.6.1.2

Add $0$ and $y$ .

$y = 12$

$y = 20$

$- y = 8$

$x = 0$

$y = 0$

$y = 12$

$y = 20$

$- y = 8$

$x = 0$

$y = 0$

$y = 12$

$y = 20$

$- y = 8$

$x = 0$

$y = 0$

$y = 12$

$y = 20$

$- y = 8$

$x = 0$

$y = 0$

Step 2

Replace all occurrences of $y$ with $12$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- y = 8$ with $12$ .

$- (12) = 8$

$y = 12$

$y = 20$

$x = 0$

$y = 0$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $- 1$ by $12$ .

$- 12 = 8$

$y = 12$

$y = 20$

$x = 0$

$y = 0$

$- 12 = 8$

$y = 12$

$y = 20$

$x = 0$

$y = 0$

$- 12 = 8$

$y = 12$

$y = 20$

$x = 0$

$y = 0$

Step 3

Since $- 12 = 8$ is not true, there is no solution.

No solution

Step 4