Finite Math Examples

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

Step 1

Subtract $y$ from both sides of the equation.

$x = 1 - y$

$x - y = 3$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $x - y = 3$ with $1 - y$ .

$(1 - y) - y = 3$

$x = 1 - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Subtract $y$ from $- y$ .

$1 - 2 y = 3$

$x = 1 - y$

$1 - 2 y = 3$

$x = 1 - y$

$1 - 2 y = 3$

$x = 1 - y$

Step 3

Solve for $y$ in $1 - 2 y = 3$ .

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Step 3.1

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1.1

Subtract $1$ from both sides of the equation.

$- 2 y = 3 - 1$

$x = 1 - y$

Step 3.1.2

Subtract $1$ from $3$ .

$- 2 y = 2$

$x = 1 - y$

$- 2 y = 2$

$x = 1 - y$

Step 3.2

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

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Step 3.2.1

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

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

$x = 1 - y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

$x = 1 - y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

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

$x = 1 - y$

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

$x = 1 - y$

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

$x = 1 - y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $2$ by $- 2$ .

$y = - 1$

$x = 1 - y$

$y = - 1$

$x = 1 - y$

$y = - 1$

$x = 1 - y$

$y = - 1$

$x = 1 - y$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

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Step 4.1

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

$x = 1 - (- 1)$

$y = - 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $1 - (- 1)$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 1$ .

$x = 1 + 1$

$y = - 1$

Step 4.2.1.2

Add $1$ and $1$ .

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

$x = 2$

$y = - 1$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(2, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 7