Find Three Ordered Pair Solutions 5x+4y=40

$5 x + 4 y = 40$

Step 1

Solve the equation for $y$ .

Subtract $5 x$ from both sides of the equation.

$4 y = 40 - 5 x$

Divide each term in $4 y = 40 - 5 x$ by $4$ and simplify.

Divide each term in $4 y = 40 - 5 x$ by $4$ .

$\frac{4 y}{4} = \frac{40}{4} + \frac{- 5 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{40}{4} + \frac{- 5 x}{4}$

Divide $y$ by $1$ .

$y = \frac{40}{4} + \frac{- 5 x}{4}$

Simplify the right side.

Simplify each term.

Divide $40$ by $4$ .

$y = 10 + \frac{- 5 x}{4}$

Move the negative in front of the fraction.

$y = 10 - \frac{5 x}{4}$

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.

$y = 10 - \frac{5 (0)}{4}$

Simplify $10 - \frac{5 (0)}{4}$ .

Simplify each term.

Cancel the common factor of $0$ and $4$ .

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

$y = 10 - \frac{4 (5 \cdot (0))}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$y = 10 - \frac{4 (5 \cdot (0))}{4 (1)}$

Cancel the common factor.

$y = 10 - \frac{4 (5 \cdot (0))}{4 \cdot 1}$

Rewrite the expression.

$y = 10 - \frac{5 \cdot (0)}{1}$

Divide $5 \cdot (0)$ by $1$ .

$y = 10 - (5 \cdot (0))$

Multiply $- (5 \cdot (0))$ .

Multiply $5$ by $0$ .

$y = 10 - 0$

Multiply $- 1$ by $0$ .

$y = 10 + 0$

Add $10$ and $0$ .

$y = 10$

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

$(0, 10)$

Step 4

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

Remove parentheses.

$y = 10 - \frac{5 (1)}{4}$

Simplify $10 - \frac{5 (1)}{4}$ .

Multiply $5$ by $1$ .

$y = 10 - \frac{5}{4}$

To write $10$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = 10 \cdot \frac{4}{4} - \frac{5}{4}$

Combine $10$ and $\frac{4}{4}$ .

$y = \frac{10 \cdot 4}{4} - \frac{5}{4}$

Combine the numerators over the common denominator.

$y = \frac{10 \cdot 4 - 5}{4}$

Simplify the numerator.

Multiply $10$ by $4$ .

$y = \frac{40 - 5}{4}$

Subtract $5$ from $40$ .

$y = \frac{35}{4}$

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

$(1, \frac{35}{4})$

Step 5

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

Remove parentheses.

$y = 10 - \frac{5 (2)}{4}$

Simplify $10 - \frac{5 (2)}{4}$ .

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $5 (2)$ .

$y = 10 - \frac{2 \cdot 5}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = 10 - \frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$y = 10 - \frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$y = 10 - \frac{5}{2}$

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = 10 \cdot \frac{2}{2} - \frac{5}{2}$

Combine $10$ and $\frac{2}{2}$ .

$y = \frac{10 \cdot 2}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$y = \frac{10 \cdot 2 - 5}{2}$

Simplify the numerator.

Multiply $10$ by $2$ .

$y = \frac{20 - 5}{2}$

Subtract $5$ from $20$ .

$y = \frac{15}{2}$

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

$(2, \frac{15}{2})$

Step 6

These are three possible solutions to the equation.

$(0, 10), (1, \frac{35}{4}), (2, \frac{15}{2})$

Step 7

Find Three Ordered Pair Solutions 5x+4y=40

Related Questions

Support LCMGCF.com by disabling your adblocker.