Finite Math Examples

$3 y = - 2 x + 100$ , $4 y = - 5 x + 200$

Step 1

Divide each term in $3 y = - 2 x + 100$ by $3$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $3 y = - 2 x + 100$ by $3$ .

$\frac{3 y}{3} = \frac{- 2 x}{3} + \frac{100}{3}$

$4 y = - 5 x + 200$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 2 x}{3} + \frac{100}{3}$

$4 y = - 5 x + 200$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 2 x}{3} + \frac{100}{3}$

$4 y = - 5 x + 200$

$y = \frac{- 2 x}{3} + \frac{100}{3}$

$4 y = - 5 x + 200$

$y = \frac{- 2 x}{3} + \frac{100}{3}$

$4 y = - 5 x + 200$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Move the negative in front of the fraction.

$y = - \frac{2 x}{3} + \frac{100}{3}$

$4 y = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$4 y = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$4 y = - 5 x + 200$

Step 2

Replace all occurrences of $y$ with $- \frac{2 x}{3} + \frac{100}{3}$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $y$ in $4 y = - 5 x + 200$ with $- \frac{2 x}{3} + \frac{100}{3}$ .

$4 (- \frac{2 x}{3} + \frac{100}{3}) = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $4 (- \frac{2 x}{3} + \frac{100}{3})$ .

Tap for more steps...

Step 2.2.1.1

Apply the distributive property.

$4 (- \frac{2 x}{3}) + 4 (\frac{100}{3}) = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 2.2.1.2

Multiply $4 (- \frac{2 x}{3})$ .

Tap for more steps...

Step 2.2.1.2.1

Multiply $- 1$ by $4$ .

$- 4 \frac{2 x}{3} + 4 (\frac{100}{3}) = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 2.2.1.2.2

Combine $- 4$ and $\frac{2 x}{3}$ .

$\frac{- 4 (2 x)}{3} + 4 (\frac{100}{3}) = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 2.2.1.2.3

Multiply $2$ by $- 4$ .

$\frac{- 8 x}{3} + 4 (\frac{100}{3}) = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$\frac{- 8 x}{3} + 4 (\frac{100}{3}) = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 2.2.1.3

Multiply $4 (\frac{100}{3})$ .

Tap for more steps...

Step 2.2.1.3.1

Combine $4$ and $\frac{100}{3}$ .

$\frac{- 8 x}{3} + \frac{4 \cdot 100}{3} = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 2.2.1.3.2

Multiply $4$ by $100$ .

$\frac{- 8 x}{3} + \frac{400}{3} = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$\frac{- 8 x}{3} + \frac{400}{3} = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 2.2.1.4

Move the negative in front of the fraction.

$- \frac{8 x}{3} + \frac{400}{3} = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$- \frac{8 x}{3} + \frac{400}{3} = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$- \frac{8 x}{3} + \frac{400}{3} = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$- \frac{8 x}{3} + \frac{400}{3} = - 5 x + 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3

Solve for $x$ in $- \frac{8 x}{3} + \frac{400}{3} = - 5 x + 200$ .

Tap for more steps...

Step 3.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1.1

Add $5 x$ to both sides of the equation.

$- \frac{8 x}{3} + \frac{400}{3} + 5 x = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.1.2

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{8 x}{3} + 5 x \cdot \frac{3}{3} + \frac{400}{3} = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.1.3

Combine $5 x$ and $\frac{3}{3}$ .

$- \frac{8 x}{3} + \frac{5 x \cdot 3}{3} + \frac{400}{3} = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{- 8 x + 5 x \cdot 3}{3} + \frac{400}{3} = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.1.5

Combine the numerators over the common denominator.

$\frac{- 8 x + 5 x \cdot 3 + 400}{3} = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.1.6

Multiply $3$ by $5$ .

$\frac{- 8 x + 15 x + 400}{3} = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.1.7

Add $- 8 x$ and $15 x$ .

$\frac{7 x + 400}{3} = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$\frac{7 x + 400}{3} = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.2

Multiply both sides by $3$ .

$\frac{7 x + 400}{3} \cdot 3 = 200 \cdot 3$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.3

Simplify.

Tap for more steps...

Step 3.3.1

Simplify the left side.

Tap for more steps...

Step 3.3.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.1.1.1

Cancel the common factor.

$\frac{7 x + 400}{3} \cdot 3 = 200 \cdot 3$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.3.1.1.2

Rewrite the expression.

$7 x + 400 = 200 \cdot 3$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$7 x + 400 = 200 \cdot 3$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$7 x + 400 = 200 \cdot 3$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.3.2

Simplify the right side.

Tap for more steps...

Step 3.3.2.1

Multiply $200$ by $3$ .

$7 x + 400 = 600$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$7 x + 400 = 600$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$7 x + 400 = 600$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.4

Solve for $x$ .

Tap for more steps...

Step 3.4.1

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

Tap for more steps...

Step 3.4.1.1

Subtract $400$ from both sides of the equation.

$7 x = 600 - 400$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.4.1.2

Subtract $400$ from $600$ .

$7 x = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$7 x = 200$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.4.2

Divide each term in $7 x = 200$ by $7$ and simplify.

Tap for more steps...

Step 3.4.2.1

Divide each term in $7 x = 200$ by $7$ .

$\frac{7 x}{7} = \frac{200}{7}$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.4.2.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 3.4.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{200}{7}$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 3.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{200}{7}$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$x = \frac{200}{7}$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$x = \frac{200}{7}$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$x = \frac{200}{7}$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$x = \frac{200}{7}$

$y = - \frac{2 x}{3} + \frac{100}{3}$

$x = \frac{200}{7}$

$y = - \frac{2 x}{3} + \frac{100}{3}$

Step 4

Replace all occurrences of $x$ with $\frac{200}{7}$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $x$ in $y = - \frac{2 x}{3} + \frac{100}{3}$ with $\frac{200}{7}$ .

$y = - \frac{2 (\frac{200}{7})}{3} + \frac{100}{3}$

$x = \frac{200}{7}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- \frac{2 (\frac{200}{7})}{3} + \frac{100}{3}$ .

Tap for more steps...

Step 4.2.1.1

Combine the numerators over the common denominator.

$y = \frac{- 2 (\frac{200}{7}) + 100}{3}$

$x = \frac{200}{7}$

Step 4.2.1.2

Simplify each term.

Tap for more steps...

Step 4.2.1.2.1

Multiply $- 2 (\frac{200}{7})$ .

Tap for more steps...

Step 4.2.1.2.1.1

Combine $- 2$ and $\frac{200}{7}$ .

$y = \frac{\frac{- 2 \cdot 200}{7} + 100}{3}$

$x = \frac{200}{7}$

Step 4.2.1.2.1.2

Multiply $- 2$ by $200$ .

$y = \frac{\frac{- 400}{7} + 100}{3}$

$x = \frac{200}{7}$

$y = \frac{\frac{- 400}{7} + 100}{3}$

$x = \frac{200}{7}$

Step 4.2.1.2.2

Move the negative in front of the fraction.

$y = \frac{- \frac{400}{7} + 100}{3}$

$x = \frac{200}{7}$

$y = \frac{- \frac{400}{7} + 100}{3}$

$x = \frac{200}{7}$

Step 4.2.1.3

To write $100$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = \frac{- \frac{400}{7} + 100 \cdot \frac{7}{7}}{3}$

$x = \frac{200}{7}$

Step 4.2.1.4

Combine $100$ and $\frac{7}{7}$ .

$y = \frac{- \frac{400}{7} + \frac{100 \cdot 7}{7}}{3}$

$x = \frac{200}{7}$

Step 4.2.1.5

Combine the numerators over the common denominator.

$y = \frac{\frac{- 400 + 100 \cdot 7}{7}}{3}$

$x = \frac{200}{7}$

Step 4.2.1.6

Simplify the numerator.

Tap for more steps...

Step 4.2.1.6.1

Multiply $100$ by $7$ .

$y = \frac{\frac{- 400 + 700}{7}}{3}$

$x = \frac{200}{7}$

Step 4.2.1.6.2

Add $- 400$ and $700$ .

$y = \frac{\frac{300}{7}}{3}$

$x = \frac{200}{7}$

$y = \frac{\frac{300}{7}}{3}$

$x = \frac{200}{7}$

Step 4.2.1.7

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{300}{7} \cdot \frac{1}{3}$

$x = \frac{200}{7}$

Step 4.2.1.8

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.8.1

Factor $3$ out of $300$ .

$y = \frac{3 (100)}{7} \cdot \frac{1}{3}$

$x = \frac{200}{7}$

Step 4.2.1.8.2

Cancel the common factor.

$y = \frac{3 \cdot 100}{7} \cdot \frac{1}{3}$

$x = \frac{200}{7}$

Step 4.2.1.8.3

Rewrite the expression.

$y = \frac{100}{7}$

$x = \frac{200}{7}$

$y = \frac{100}{7}$

$x = \frac{200}{7}$

$y = \frac{100}{7}$

$x = \frac{200}{7}$

$y = \frac{100}{7}$

$x = \frac{200}{7}$

$y = \frac{100}{7}$

$x = \frac{200}{7}$

Step 5

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

$(\frac{200}{7}, \frac{100}{7})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{200}{7}, \frac{100}{7})$

Equation Form:

$x = \frac{200}{7}, y = \frac{100}{7}$

Step 7