Find Three Ordered Pair Solutions 6x+7y=42

$6 x + 7 y = 42$

Step 1

Solve the equation for $y$ .

Subtract $6 x$ from both sides of the equation.

$7 y = 42 - 6 x$

Divide each term in $7 y = 42 - 6 x$ by $7$ and simplify.

Divide each term in $7 y = 42 - 6 x$ by $7$ .

$\frac{7 y}{7} = \frac{42}{7} + \frac{- 6 x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{42}{7} + \frac{- 6 x}{7}$

Divide $y$ by $1$ .

$y = \frac{42}{7} + \frac{- 6 x}{7}$

Simplify the right side.

Simplify each term.

Divide $42$ by $7$ .

$y = 6 + \frac{- 6 x}{7}$

Move the negative in front of the fraction.

$y = 6 - \frac{6 x}{7}$

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.

$y = 6 - \frac{6 (0)}{7}$

Simplify $6 - \frac{6 (0)}{7}$ .

Simplify each term.

Cancel the common factor of $0$ and $7$ .

Factor $7$ out of $6 (0)$ .

$y = 6 - \frac{7 (6 \cdot (0))}{7}$

Cancel the common factors.

Factor $7$ out of $7$ .

$y = 6 - \frac{7 (6 \cdot (0))}{7 (1)}$

Cancel the common factor.

$y = 6 - \frac{7 (6 \cdot (0))}{7 \cdot 1}$

Rewrite the expression.

$y = 6 - \frac{6 \cdot (0)}{1}$

Divide $6 \cdot (0)$ by $1$ .

$y = 6 - (6 \cdot (0))$

Multiply $- (6 \cdot (0))$ .

Multiply $6$ by $0$ .

$y = 6 - 0$

Multiply $- 1$ by $0$ .

$y = 6 + 0$

Add $6$ and $0$ .

$y = 6$

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

$(0, 6)$

Step 4

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

Remove parentheses.

$y = 6 - \frac{6 (1)}{7}$

Simplify $6 - \frac{6 (1)}{7}$ .

Multiply $6$ by $1$ .

$y = 6 - \frac{6}{7}$

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = 6 \cdot \frac{7}{7} - \frac{6}{7}$

Combine $6$ and $\frac{7}{7}$ .

$y = \frac{6 \cdot 7}{7} - \frac{6}{7}$

Combine the numerators over the common denominator.

$y = \frac{6 \cdot 7 - 6}{7}$

Simplify the numerator.

Multiply $6$ by $7$ .

$y = \frac{42 - 6}{7}$

Subtract $6$ from $42$ .

$y = \frac{36}{7}$

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

$(1, \frac{36}{7})$

Step 5

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

Remove parentheses.

$y = 6 - \frac{6 (2)}{7}$

Simplify $6 - \frac{6 (2)}{7}$ .

Multiply $6$ by $2$ .

$y = 6 - \frac{12}{7}$

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = 6 \cdot \frac{7}{7} - \frac{12}{7}$

Combine $6$ and $\frac{7}{7}$ .

$y = \frac{6 \cdot 7}{7} - \frac{12}{7}$

Combine the numerators over the common denominator.

$y = \frac{6 \cdot 7 - 12}{7}$

Simplify the numerator.

Multiply $6$ by $7$ .

$y = \frac{42 - 12}{7}$

Subtract $12$ from $42$ .

$y = \frac{30}{7}$

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

$(2, \frac{30}{7})$

Step 6

These are three possible solutions to the equation.

$(0, 6), (1, \frac{36}{7}), (2, \frac{30}{7})$

Step 7

Find Three Ordered Pair Solutions 6x+7y=42

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