Find Three Ordered Pair Solutions 4x+3y=10

$4 x + 3 y = 10$

Step 1

Solve the equation for $y$ .

Subtract $4 x$ from both sides of the equation.

$3 y = 10 - 4 x$

Divide each term in $3 y = 10 - 4 x$ by $3$ and simplify.

Divide each term in $3 y = 10 - 4 x$ by $3$ .

$\frac{3 y}{3} = \frac{10}{3} + \frac{- 4 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{10}{3} + \frac{- 4 x}{3}$

Divide $y$ by $1$ .

$y = \frac{10}{3} + \frac{- 4 x}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{10}{3} - \frac{4 x}{3}$

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.

$y = \frac{10}{3} - \frac{4 (0)}{3}$

Simplify $\frac{10}{3} - \frac{4 (0)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{10 - 4 \cdot 0}{3}$

Simplify the expression.

Multiply $- 4$ by $0$ .

$y = \frac{10 + 0}{3}$

Add $10$ and $0$ .

$y = \frac{10}{3}$

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

$(0, \frac{10}{3})$

Step 4

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

Remove parentheses.

$y = \frac{10}{3} - \frac{4 (1)}{3}$

Simplify $\frac{10}{3} - \frac{4 (1)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{10 - 4 \cdot 1}{3}$

Simplify the expression.

Multiply $- 4$ by $1$ .

$y = \frac{10 - 4}{3}$

Subtract $4$ from $10$ .

$y = \frac{6}{3}$

Divide $6$ by $3$ .

$y = 2$

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

$(1, 2)$

Step 5

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

Remove parentheses.

$y = \frac{10}{3} - \frac{4 (2)}{3}$

Simplify $\frac{10}{3} - \frac{4 (2)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{10 - 4 \cdot 2}{3}$

Simplify the expression.

Multiply $- 4$ by $2$ .

$y = \frac{10 - 8}{3}$

Subtract $8$ from $10$ .

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

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

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

Step 6

These are three possible solutions to the equation.

$(0, \frac{10}{3}), (1, 2), (2, \frac{2}{3})$

Step 7

Find Three Ordered Pair Solutions 4x+3y=10

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