Finite Math Examples

$2 x - 7 y = - 14$ , $2 x + 2 y = 13$

Step 1

Solve for $x$ in $2 x - 7 y = - 14$ .

Tap for more steps...

Step 1.1

Add $7 y$ to both sides of the equation.

$2 x = - 14 + 7 y$

$2 x + 2 y = 13$

Step 1.2

Divide each term in $2 x = - 14 + 7 y$ by $2$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $2 x = - 14 + 7 y$ by $2$ .

$\frac{2 x}{2} = \frac{- 14}{2} + \frac{7 y}{2}$

$2 x + 2 y = 13$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 14}{2} + \frac{7 y}{2}$

$2 x + 2 y = 13$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 14}{2} + \frac{7 y}{2}$

$2 x + 2 y = 13$

$x = \frac{- 14}{2} + \frac{7 y}{2}$

$2 x + 2 y = 13$

$x = \frac{- 14}{2} + \frac{7 y}{2}$

$2 x + 2 y = 13$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Divide $- 14$ by $2$ .

$x = - 7 + \frac{7 y}{2}$

$2 x + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

$2 x + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

$2 x + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

$2 x + 2 y = 13$

Step 2

Replace all occurrences of $x$ with $- 7 + \frac{7 y}{2}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $2 x + 2 y = 13$ with $- 7 + \frac{7 y}{2}$ .

$2 (- 7 + \frac{7 y}{2}) + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $2 (- 7 + \frac{7 y}{2}) + 2 y$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$2 \cdot - 7 + 2 (\frac{7 y}{2}) + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

Step 2.2.1.1.2

Multiply $2$ by $- 7$ .

$- 14 + 2 (\frac{7 y}{2}) + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

Step 2.2.1.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.3.1

Cancel the common factor.

$- 14 + 2 (\frac{7 y}{2}) + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

Step 2.2.1.1.3.2

Rewrite the expression.

$- 14 + 7 y + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

$- 14 + 7 y + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

$- 14 + 7 y + 2 y = 13$

$x = - 7 + \frac{7 y}{2}$

Step 2.2.1.2

Add $7 y$ and $2 y$ .

$- 14 + 9 y = 13$

$x = - 7 + \frac{7 y}{2}$

$- 14 + 9 y = 13$

$x = - 7 + \frac{7 y}{2}$

$- 14 + 9 y = 13$

$x = - 7 + \frac{7 y}{2}$

$- 14 + 9 y = 13$

$x = - 7 + \frac{7 y}{2}$

Step 3

Solve for $y$ in $- 14 + 9 y = 13$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Add $14$ to both sides of the equation.

$9 y = 13 + 14$

$x = - 7 + \frac{7 y}{2}$

Step 3.1.2

Add $13$ and $14$ .

$9 y = 27$

$x = - 7 + \frac{7 y}{2}$

$9 y = 27$

$x = - 7 + \frac{7 y}{2}$

Step 3.2

Divide each term in $9 y = 27$ by $9$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $9 y = 27$ by $9$ .

$\frac{9 y}{9} = \frac{27}{9}$

$x = - 7 + \frac{7 y}{2}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{27}{9}$

$x = - 7 + \frac{7 y}{2}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{27}{9}$

$x = - 7 + \frac{7 y}{2}$

$y = \frac{27}{9}$

$x = - 7 + \frac{7 y}{2}$

$y = \frac{27}{9}$

$x = - 7 + \frac{7 y}{2}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $27$ by $9$ .

$y = 3$

$x = - 7 + \frac{7 y}{2}$

$y = 3$

$x = - 7 + \frac{7 y}{2}$

$y = 3$

$x = - 7 + \frac{7 y}{2}$

$y = 3$

$x = - 7 + \frac{7 y}{2}$

Step 4

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

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $x = - 7 + \frac{7 y}{2}$ with $3$ .

$x = - 7 + \frac{7 (3)}{2}$

$y = 3$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- 7 + \frac{7 (3)}{2}$ .

Tap for more steps...

Step 4.2.1.1

Multiply $7$ by $3$ .

$x = - 7 + \frac{21}{2}$

$y = 3$

Step 4.2.1.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - 7 \cdot \frac{2}{2} + \frac{21}{2}$

$y = 3$

Step 4.2.1.3

Combine $- 7$ and $\frac{2}{2}$ .

$x = \frac{- 7 \cdot 2}{2} + \frac{21}{2}$

$y = 3$

Step 4.2.1.4

Combine the numerators over the common denominator.

$x = \frac{- 7 \cdot 2 + 21}{2}$

$y = 3$

Step 4.2.1.5

Simplify the numerator.

Tap for more steps...

Step 4.2.1.5.1

Multiply $- 7$ by $2$ .

$x = \frac{- 14 + 21}{2}$

$y = 3$

Step 4.2.1.5.2

Add $- 14$ and $21$ .

$x = \frac{7}{2}$

$y = 3$

$x = \frac{7}{2}$

$y = 3$

$x = \frac{7}{2}$

$y = 3$

$x = \frac{7}{2}$

$y = 3$

$x = \frac{7}{2}$

$y = 3$

Step 5

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

$(\frac{7}{2}, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{7}{2}, 3)$

Equation Form:

$x = \frac{7}{2}, y = 3$

Step 7