Finite Math Examples

$- x + 5 y = 8$ , $x + y = 2$ , $y = 0$

Step 1

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

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Step 1.1

Replace all occurrences of $y$ in $- x + 5 y = 8$ with $0$ .

$- x + 5 (0) = 8$

$y = 0$

$x + y = 2$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $- x + 5 (0)$ .

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Step 1.2.1.1

Multiply $5$ by $0$ .

$- x + 0 = 8$

$y = 0$

$x + y = 2$

Step 1.2.1.2

Add $- x$ and $0$ .

$- x = 8$

$y = 0$

$x + y = 2$

$- x = 8$

$y = 0$

$x + y = 2$

$- x = 8$

$y = 0$

$x + y = 2$

Step 1.3

Replace all occurrences of $y$ in $x + y = 2$ with $0$ .

$x + 0 = 2$

$- x = 8$

$y = 0$

Step 1.4

Simplify the left side.

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Step 1.4.1

Simplify $x + 0$ .

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Step 1.4.1.1

Remove parentheses.

$x + 0 = 2$

$- x = 8$

$y = 0$

Step 1.4.1.2

Add $x$ and $0$ .

$x = 2$

$- x = 8$

$y = 0$

$x = 2$

$- x = 8$

$y = 0$

$x = 2$

$- x = 8$

$y = 0$

$x = 2$

$- x = 8$

$y = 0$

Step 2

Replace all occurrences of $x$ with $2$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- x = 8$ with $2$ .

$- (2) = 8$

$x = 2$

$y = 0$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $- 1$ by $2$ .

$- 2 = 8$

$x = 2$

$y = 0$

$- 2 = 8$

$x = 2$

$y = 0$

$- 2 = 8$

$x = 2$

$y = 0$

Step 3

Since $- 2 = 8$ is not true, there is no solution.

No solution

Step 4