Find Three Ordered Pair Solutions 2x+3y=5x-y

$2 x + 3 y = 5 x - y$

Step 1

Solve the equation for $y$ .

Move all terms containing $y$ to the left side of the equation.

Add $y$ to both sides of the equation.

$2 x + 3 y + y = 5 x$

Add $3 y$ and $y$ .

$2 x + 4 y = 5 x$

Move all terms not containing $y$ to the right side of the equation.

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

$4 y = 5 x - 2 x$

Subtract $2 x$ from $5 x$ .

$4 y = 3 x$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

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.

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

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

Cancel the common factor of $0$ and $4$ .

Factor $4$ out of $3 (0)$ .

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

Cancel the common factors.

Factor $4$ out of $4$ .

$y = \frac{4 (3 \cdot (0))}{4 (1)}$

Cancel the common factor.

$y = \frac{4 (3 \cdot (0))}{4 \cdot 1}$

Rewrite the expression.

$y = \frac{3 \cdot (0)}{1}$

Divide $3 \cdot (0)$ by $1$ .

$y = 3 \cdot (0)$

Multiply $3$ by $0$ .

$y = 0$

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

$(0, 0)$

Step 4

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

Remove parentheses.

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

Multiply $3$ by $1$ .

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

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

$(1, \frac{3}{4})$

Step 5

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

Remove parentheses.

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

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $3 (2)$ .

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

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.

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

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

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

Step 6

These are three possible solutions to the equation.

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

Step 7

Find Three Ordered Pair Solutions 2x+3y=5x-y

Related Questions

Support LCMGCF.com by disabling your adblocker.