Find Three Ordered Pair Solutions 2x+5y=19

$2 x + 5 y = 19$

Step 1

Solve the equation for $y$ .

Subtract $2 x$ from both sides of the equation.

$5 y = 19 - 2 x$

Divide each term in $5 y = 19 - 2 x$ by $5$ and simplify.

Divide each term in $5 y = 19 - 2 x$ by $5$ .

$\frac{5 y}{5} = \frac{19}{5} + \frac{- 2 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{19}{5} + \frac{- 2 x}{5}$

Divide $y$ by $1$ .

$y = \frac{19}{5} + \frac{- 2 x}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{19}{5} - \frac{2 x}{5}$

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.

$y = \frac{19}{5} - \frac{2 (0)}{5}$

Simplify $\frac{19}{5} - \frac{2 (0)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{19 - 2 \cdot 0}{5}$

Simplify the expression.

Multiply $- 2$ by $0$ .

$y = \frac{19 + 0}{5}$

Add $19$ and $0$ .

$y = \frac{19}{5}$

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

$(0, \frac{19}{5})$

Step 4

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

Remove parentheses.

$y = \frac{19}{5} - \frac{2 (1)}{5}$

Simplify $\frac{19}{5} - \frac{2 (1)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{19 - 2 \cdot 1}{5}$

Simplify the expression.

Multiply $- 2$ by $1$ .

$y = \frac{19 - 2}{5}$

Subtract $2$ from $19$ .

$y = \frac{17}{5}$

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

$(1, \frac{17}{5})$

Step 5

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

Remove parentheses.

$y = \frac{19}{5} - \frac{2 (2)}{5}$

Simplify $\frac{19}{5} - \frac{2 (2)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{19 - 2 \cdot 2}{5}$

Simplify the expression.

Multiply $- 2$ by $2$ .

$y = \frac{19 - 4}{5}$

Subtract $4$ from $19$ .

$y = \frac{15}{5}$

Divide $15$ by $5$ .

$y = 3$

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

$(2, 3)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{19}{5}), (1, \frac{17}{5}), (2, 3)$

Step 7

Find Three Ordered Pair Solutions 2x+5y=19

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