Solve the System of Equations 9x+2y=5 y-2x+3=0

$9 x + 2 y = 5$ $y - 2 x + 3 = 0$

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

Add $2 x$ to both sides of the equation.

$y + 3 = 2 x$

$9 x + 2 y = 5$

Subtract $3$ from both sides of the equation.

$y = 2 x - 3$

$9 x + 2 y = 5$

$y = 2 x - 3$

$9 x + 2 y = 5$

Replace all occurrences of $y$ with $2 x - 3$ in each equation.

Replace all occurrences of $y$ in $9 x + 2 y = 5$ with $2 x - 3$ .

$9 x + 2 (2 x - 3) = 5$

$y = 2 x - 3$

Simplify the left side.

Simplify $9 x + 2 (2 x - 3)$ .

Simplify each term.

Apply the distributive property.

$9 x + 2 (2 x) + 2 \cdot - 3 = 5$

$y = 2 x - 3$

Multiply $2$ by $2$ .

$9 x + 4 x + 2 \cdot - 3 = 5$

$y = 2 x - 3$

Multiply $2$ by $- 3$ .

$9 x + 4 x - 6 = 5$

$y = 2 x - 3$

$9 x + 4 x - 6 = 5$

$y = 2 x - 3$

Add $9 x$ and $4 x$ .

$13 x - 6 = 5$

$y = 2 x - 3$

$13 x - 6 = 5$

$y = 2 x - 3$

$13 x - 6 = 5$

$y = 2 x - 3$

$13 x - 6 = 5$

$y = 2 x - 3$

Solve for $x$ in $13 x - 6 = 5$ .

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

Add $6$ to both sides of the equation.

$13 x = 5 + 6$

$y = 2 x - 3$

Add $5$ and $6$ .

$13 x = 11$

$y = 2 x - 3$

$13 x = 11$

$y = 2 x - 3$

Divide each term in $13 x = 11$ by $13$ and simplify.

Divide each term in $13 x = 11$ by $13$ .

$\frac{13 x}{13} = \frac{11}{13}$

$y = 2 x - 3$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{11}{13}$

$y = 2 x - 3$

Divide $x$ by $1$ .

$x = \frac{11}{13}$

$y = 2 x - 3$

$x = \frac{11}{13}$

$y = 2 x - 3$

$x = \frac{11}{13}$

$y = 2 x - 3$

$x = \frac{11}{13}$

$y = 2 x - 3$

$x = \frac{11}{13}$

$y = 2 x - 3$

Replace all occurrences of $x$ with $\frac{11}{13}$ in each equation.

Replace all occurrences of $x$ in $y = 2 x - 3$ with $\frac{11}{13}$ .

$y = 2 (\frac{11}{13}) - 3$

$x = \frac{11}{13}$

Simplify the right side.

Simplify $2 (\frac{11}{13}) - 3$ .

Multiply $2 (\frac{11}{13})$ .

Combine $2$ and $\frac{11}{13}$ .

$y = \frac{2 \cdot 11}{13} - 3$

$x = \frac{11}{13}$

Multiply $2$ by $11$ .

$y = \frac{22}{13} - 3$

$x = \frac{11}{13}$

$y = \frac{22}{13} - 3$

$x = \frac{11}{13}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$y = \frac{22}{13} - 3 \cdot \frac{13}{13}$

$x = \frac{11}{13}$

Combine $- 3$ and $\frac{13}{13}$ .

$y = \frac{22}{13} + \frac{- 3 \cdot 13}{13}$

$x = \frac{11}{13}$

Combine the numerators over the common denominator.

$y = \frac{22 - 3 \cdot 13}{13}$

$x = \frac{11}{13}$

Simplify the numerator.

Multiply $- 3$ by $13$ .

$y = \frac{22 - 39}{13}$

$x = \frac{11}{13}$

Subtract $39$ from $22$ .

$y = \frac{- 17}{13}$

$x = \frac{11}{13}$

$y = \frac{- 17}{13}$

$x = \frac{11}{13}$

Move the negative in front of the fraction.

$y = - \frac{17}{13}$

$x = \frac{11}{13}$

$y = - \frac{17}{13}$

$x = \frac{11}{13}$

$y = - \frac{17}{13}$

$x = \frac{11}{13}$

$y = - \frac{17}{13}$

$x = \frac{11}{13}$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(\frac{11}{13}, - \frac{17}{13})$

The result can be shown in multiple forms.

Point Form:

$(\frac{11}{13}, - \frac{17}{13})$

Equation Form:

$x = \frac{11}{13}, y = - \frac{17}{13}$

Solve the System of Equations 9x+2y=5 y-2x+3=0

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