Finite Math Examples

$x + y = 0$ , $3 x - y = 5$ , $x - y = - 1$

Step 1

Subtract $y$ from both sides of the equation.

$x = - y$

$3 x - y = 5$

$x - y = - 1$

Step 2

Replace all occurrences of $x$ with $- y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $3 x - y = 5$ with $- y$ .

$3 (- y) - y = 5$

$x = - y$

$x - y = - 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (- y) - y$ .

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Step 2.2.1.1

Multiply $- 1$ by $3$ .

$- 3 y - y = 5$

$x = - y$

$x - y = - 1$

Step 2.2.1.2

Subtract $y$ from $- 3 y$ .

$- 4 y = 5$

$x = - y$

$x - y = - 1$

$- 4 y = 5$

$x = - y$

$x - y = - 1$

$- 4 y = 5$

$x = - y$

$x - y = - 1$

Step 2.3

Replace all occurrences of $x$ in $x - y = - 1$ with $- y$ .

$(- y) - y = - 1$

$- 4 y = 5$

$x = - y$

Step 2.4

Simplify the left side.

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Step 2.4.1

Subtract $y$ from $- y$ .

$- 2 y = - 1$

$- 4 y = 5$

$x = - y$

$- 2 y = - 1$

$- 4 y = 5$

$x = - y$

$- 2 y = - 1$

$- 4 y = 5$

$x = - y$

Step 3

Divide each term in $- 2 y = - 1$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 y = - 1$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 1}{- 2}$

$- 4 y = 5$

$x = - y$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 1}{- 2}$

$- 4 y = 5$

$x = - y$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 1}{- 2}$

$- 4 y = 5$

$x = - y$

$y = \frac{- 1}{- 2}$

$- 4 y = 5$

$x = - y$

$y = \frac{- 1}{- 2}$

$- 4 y = 5$

$x = - y$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$y = \frac{1}{2}$

$- 4 y = 5$

$x = - y$

$y = \frac{1}{2}$

$- 4 y = 5$

$x = - y$

$y = \frac{1}{2}$

$- 4 y = 5$

$x = - y$

Step 4

Replace all occurrences of $y$ with $\frac{1}{2}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $- 4 y = 5$ with $\frac{1}{2}$ .

$- 4 (\frac{1}{2}) = 5$

$y = \frac{1}{2}$

$x = - y$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Factor $2$ out of $- 4$ .

$2 (- 2) (\frac{1}{2}) = 5$

$y = \frac{1}{2}$

$x = - y$

Step 4.2.1.2

Cancel the common factor.

$2 \cdot (- 2 (\frac{1}{2})) = 5$

$y = \frac{1}{2}$

$x = - y$

Step 4.2.1.3

Rewrite the expression.

$- 2 = 5$

$y = \frac{1}{2}$

$x = - y$

$- 2 = 5$

$y = \frac{1}{2}$

$x = - y$

$- 2 = 5$

$y = \frac{1}{2}$

$x = - y$

Step 4.3

Replace all occurrences of $y$ in $x = - y$ with $\frac{1}{2}$ .

$x = - (\frac{1}{2})$

$- 2 = 5$

$y = \frac{1}{2}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Multiply $- 1$ by $\frac{1}{2}$ .

$x = - \frac{1}{2}$

$- 2 = 5$

$y = \frac{1}{2}$

$x = - \frac{1}{2}$

$- 2 = 5$

$y = \frac{1}{2}$

$x = - \frac{1}{2}$

$- 2 = 5$

$y = \frac{1}{2}$

Step 5

Since $- 2 = 5$ is not true, there is no solution.

No solution

Step 6