Find Three Ordered Pair Solutions 4x+5y=5000

$4 x + 5 y = 5000$

Step 1

Solve the equation for $y$ .

Subtract $4 x$ from both sides of the equation.

$5 y = 5000 - 4 x$

Divide each term in $5 y = 5000 - 4 x$ by $5$ and simplify.

Divide each term in $5 y = 5000 - 4 x$ by $5$ .

$\frac{5 y}{5} = \frac{5000}{5} + \frac{- 4 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{5000}{5} + \frac{- 4 x}{5}$

Divide $y$ by $1$ .

$y = \frac{5000}{5} + \frac{- 4 x}{5}$

Simplify the right side.

Simplify each term.

Divide $5000$ by $5$ .

$y = 1000 + \frac{- 4 x}{5}$

Move the negative in front of the fraction.

$y = 1000 - \frac{4 x}{5}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = 1000 - \frac{4 (0)}{5}$

Simplify $1000 - \frac{4 (0)}{5}$ .

Simplify each term.

Cancel the common factor of $0$ and $5$ .

Factor $5$ out of $4 (0)$ .

$y = 1000 - \frac{5 (4 \cdot (0))}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$y = 1000 - \frac{5 (4 \cdot (0))}{5 (1)}$

Cancel the common factor.

$y = 1000 - \frac{5 (4 \cdot (0))}{5 \cdot 1}$

Rewrite the expression.

$y = 1000 - \frac{4 \cdot (0)}{1}$

Divide $4 \cdot (0)$ by $1$ .

$y = 1000 - (4 \cdot (0))$

Multiply $- (4 \cdot (0))$ .

Multiply $4$ by $0$ .

$y = 1000 - 0$

Multiply $- 1$ by $0$ .

$y = 1000 + 0$

Add $1000$ and $0$ .

$y = 1000$

Use the $x$ and $y$ values to form the ordered pair.

$(0, 1000)$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = 1000 - \frac{4 (1)}{5}$

Simplify $1000 - \frac{4 (1)}{5}$ .

Multiply $4$ by $1$ .

$y = 1000 - \frac{4}{5}$

To write $1000$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = 1000 \cdot \frac{5}{5} - \frac{4}{5}$

Combine $1000$ and $\frac{5}{5}$ .

$y = \frac{1000 \cdot 5}{5} - \frac{4}{5}$

Combine the numerators over the common denominator.

$y = \frac{1000 \cdot 5 - 4}{5}$

Simplify the numerator.

Multiply $1000$ by $5$ .

$y = \frac{5000 - 4}{5}$

Subtract $4$ from $5000$ .

$y = \frac{4996}{5}$

Use the $x$ and $y$ values to form the ordered pair.

$(1, \frac{4996}{5})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = 1000 - \frac{4 (2)}{5}$

Simplify $1000 - \frac{4 (2)}{5}$ .

Multiply $4$ by $2$ .

$y = 1000 - \frac{8}{5}$

To write $1000$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = 1000 \cdot \frac{5}{5} - \frac{8}{5}$

Combine $1000$ and $\frac{5}{5}$ .

$y = \frac{1000 \cdot 5}{5} - \frac{8}{5}$

Combine the numerators over the common denominator.

$y = \frac{1000 \cdot 5 - 8}{5}$

Simplify the numerator.

Multiply $1000$ by $5$ .

$y = \frac{5000 - 8}{5}$

Subtract $8$ from $5000$ .

$y = \frac{4992}{5}$

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{4992}{5})$

Step 6

These are three possible solutions to the equation.

$(0, 1000), (1, \frac{4996}{5}), (2, \frac{4992}{5})$

Step 7

Find Three Ordered Pair Solutions 4x+5y=5000

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