Find Three Ordered Pair Solutions 5x-4y=17

$5 x - 4 y = 17$

Step 1

Solve the equation for $y$ .

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

$- 4 y = 17 - 5 x$

Divide each term in $- 4 y = 17 - 5 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 17 - 5 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{17}{- 4} + \frac{- 5 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{17}{- 4} + \frac{- 5 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{17}{- 4} + \frac{- 5 x}{- 4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{17}{4} + \frac{- 5 x}{- 4}$

Dividing two negative values results in a positive value.

$y = - \frac{17}{4} + \frac{5 x}{4}$

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.

$y = - \frac{17}{4} + \frac{5 (0)}{4}$

Simplify $- \frac{17}{4} + \frac{5 (0)}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 17 + 5 (0)}{4}$

Simplify the expression.

Multiply $5$ by $0$ .

$y = \frac{- 17 + 0}{4}$

Add $- 17$ and $0$ .

$y = \frac{- 17}{4}$

Move the negative in front of the fraction.

$y = - \frac{17}{4}$

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

$(0, - \frac{17}{4})$

Step 4

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

Remove parentheses.

$y = - \frac{17}{4} + \frac{5 (1)}{4}$

Simplify $- \frac{17}{4} + \frac{5 (1)}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 17 + 5 (1)}{4}$

Simplify the expression.

Multiply $5$ by $1$ .

$y = \frac{- 17 + 5}{4}$

Add $- 17$ and $5$ .

$y = \frac{- 12}{4}$

Divide $- 12$ by $4$ .

$y = - 3$

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

$(1, - 3)$

Step 5

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

Remove parentheses.

$y = - \frac{17}{4} + \frac{5 (2)}{4}$

Simplify $- \frac{17}{4} + \frac{5 (2)}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 17 + 5 (2)}{4}$

Simplify the expression.

Multiply $5$ by $2$ .

$y = \frac{- 17 + 10}{4}$

Add $- 17$ and $10$ .

$y = \frac{- 7}{4}$

Move the negative in front of the fraction.

$y = - \frac{7}{4}$

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

$(2, - \frac{7}{4})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{17}{4}), (1, - 3), (2, - \frac{7}{4})$

Step 7

Find Three Ordered Pair Solutions 5x-4y=17

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