Find Three Ordered Pair Solutions x-4y=7

$x - 4 y = 7$

Step 1

Solve the equation for $y$ .

Subtract $x$ from both sides of the equation.

$- 4 y = 7 - x$

Divide each term in $- 4 y = 7 - x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 7 - x$ by $- 4$ .

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

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.

$y = - \frac{7}{4} + \frac{0}{4}$

Simplify $- \frac{7}{4} + \frac{0}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 7 + 0}{4}$

Add $- 7$ and $0$ .

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

Move the negative in front of the fraction.

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

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

$(0, - \frac{7}{4})$

Step 4

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

Remove parentheses.

$y = - \frac{7}{4} + \frac{1}{4}$

Simplify $- \frac{7}{4} + \frac{1}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 7 + 1}{4}$

Add $- 7$ and $1$ .

$y = \frac{- 6}{4}$

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6$ .

$y = \frac{2 (- 3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{2 \cdot - 3}{2 \cdot 2}$

Cancel the common factor.

$y = \frac{2 \cdot - 3}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{- 3}{2}$

Move the negative in front of the fraction.

$y = - \frac{3}{2}$

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

$(1, - \frac{3}{2})$

Step 5

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

Remove parentheses.

$y = - \frac{7}{4} + \frac{2}{4}$

Simplify $- \frac{7}{4} + \frac{2}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 7 + 2}{4}$

Simplify the expression.

Add $- 7$ and $2$ .

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

Move the negative in front of the fraction.

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

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

$(2, - \frac{5}{4})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{7}{4}), (1, - \frac{3}{2}), (2, - \frac{5}{4})$

Step 7

Find Three Ordered Pair Solutions x-4y=7

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