Find Three Ordered Pair Solutions 7x+4y=-23

$7 x + 4 y = - 23$

Step 1

Solve the equation for $y$ .

Subtract $7 x$ from both sides of the equation.

$4 y = - 23 - 7 x$

Divide each term in $4 y = - 23 - 7 x$ by $4$ and simplify.

Divide each term in $4 y = - 23 - 7 x$ by $4$ .

$\frac{4 y}{4} = \frac{- 23}{4} + \frac{- 7 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 23}{4} + \frac{- 7 x}{4}$

Divide $y$ by $1$ .

$y = \frac{- 23}{4} + \frac{- 7 x}{4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{23}{4} + \frac{- 7 x}{4}$

Move the negative in front of the fraction.

$y = - \frac{23}{4} - \frac{7 x}{4}$

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.

$y = - \frac{23}{4} - \frac{7 (0)}{4}$

Simplify $- \frac{23}{4} - \frac{7 (0)}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 23 - 7 \cdot 0}{4}$

Simplify the expression.

Multiply $- 7$ by $0$ .

$y = \frac{- 23 + 0}{4}$

Add $- 23$ and $0$ .

$y = \frac{- 23}{4}$

Move the negative in front of the fraction.

$y = - \frac{23}{4}$

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

$(0, - \frac{23}{4})$

Step 4

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

Remove parentheses.

$y = - \frac{23}{4} - \frac{7 (1)}{4}$

Simplify $- \frac{23}{4} - \frac{7 (1)}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 23 - 7 \cdot 1}{4}$

Simplify the expression.

Multiply $- 7$ by $1$ .

$y = \frac{- 23 - 7}{4}$

Subtract $7$ from $- 23$ .

$y = \frac{- 30}{4}$

Cancel the common factor of $- 30$ and $4$ .

Factor $2$ out of $- 30$ .

$y = \frac{2 (- 15)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

$(1, - \frac{15}{2})$

Step 5

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

Remove parentheses.

$y = - \frac{23}{4} - \frac{7 (2)}{4}$

Simplify $- \frac{23}{4} - \frac{7 (2)}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{- 23 - 7 \cdot 2}{4}$

Simplify the expression.

Multiply $- 7$ by $2$ .

$y = \frac{- 23 - 14}{4}$

Subtract $14$ from $- 23$ .

$y = \frac{- 37}{4}$

Move the negative in front of the fraction.

$y = - \frac{37}{4}$

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

$(2, - \frac{37}{4})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{23}{4}), (1, - \frac{15}{2}), (2, - \frac{37}{4})$

Step 7

Find Three Ordered Pair Solutions 7x+4y=-23

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