Finite Math Examples

$x = y + 3$ , $x - 2 y = 5$

Step 1

Replace all occurrences of $x$ with $y + 3$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $x - 2 y = 5$ with $y + 3$ .

$(y + 3) - 2 y = 5$

$x = y + 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Subtract $2 y$ from $y$ .

$- y + 3 = 5$

$x = y + 3$

$- y + 3 = 5$

$x = y + 3$

$- y + 3 = 5$

$x = y + 3$

Step 2

Solve for $y$ in $- y + 3 = 5$ .

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Step 2.1

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

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Step 2.1.1

Subtract $3$ from both sides of the equation.

$- y = 5 - 3$

$x = y + 3$

Step 2.1.2

Subtract $3$ from $5$ .

$- y = 2$

$x = y + 3$

$- y = 2$

$x = y + 3$

Step 2.2

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

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Step 2.2.1

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

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

$x = y + 3$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

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

$x = y + 3$

Step 2.2.2.2

Divide $y$ by $1$ .

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

$x = y + 3$

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

$x = y + 3$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $2$ by $- 1$ .

$y = - 2$

$x = y + 3$

$y = - 2$

$x = y + 3$

$y = - 2$

$x = y + 3$

$y = - 2$

$x = y + 3$

Step 3

Replace all occurrences of $y$ with $- 2$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $x = y + 3$ with $- 2$ .

$x = (- 2) + 3$

$y = - 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Add $- 2$ and $3$ .

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

$x = 1$

$y = - 2$

Step 4

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

$(1, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, - 2)$

Equation Form:

$x = 1, y = - 2$

Step 6