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

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

Step 1

Add $x$ to both sides of the equation.

$y = - 3 + x$

$3 x + 2 y = 9$

Step 2

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

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

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

$y = - 3 + x$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = - 3 + x$

Multiply $2$ by $- 3$ .

$3 x - 6 + 2 x = 9$

$y = - 3 + x$

$3 x - 6 + 2 x = 9$

$y = - 3 + x$

Add $3 x$ and $2 x$ .

$5 x - 6 = 9$

$y = - 3 + x$

$5 x - 6 = 9$

$y = - 3 + x$

$5 x - 6 = 9$

$y = - 3 + x$

$5 x - 6 = 9$

$y = - 3 + x$

Step 3

Solve for $x$ in $5 x - 6 = 9$ .

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

Add $6$ to both sides of the equation.

$5 x = 9 + 6$

$y = - 3 + x$

Add $9$ and $6$ .

$5 x = 15$

$y = - 3 + x$

$5 x = 15$

$y = - 3 + x$

Divide each term in $5 x = 15$ by $5$ and simplify.

Divide each term in $5 x = 15$ by $5$ .

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

$y = - 3 + x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$y = - 3 + x$

Divide $x$ by $1$ .

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

$y = - 3 + x$

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

$y = - 3 + x$

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

$y = - 3 + x$

Simplify the right side.

Divide $15$ by $5$ .

$x = 3$

$y = - 3 + x$

$x = 3$

$y = - 3 + x$

$x = 3$

$y = - 3 + x$

$x = 3$

$y = - 3 + x$

Step 4

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

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

$y = - 3 + 3$

$x = 3$

Simplify $y = - 3 + 3$ .

Simplify the left side.

Remove parentheses.

$y = - 3 + 3$

$x = 3$

$y = - 3 + 3$

$x = 3$

Simplify the right side.

Add $- 3$ and $3$ .

$y = 0$

$x = 3$

$y = 0$

$x = 3$

$y = 0$

$x = 3$

$y = 0$

$x = 3$

Step 5

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

$(3, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 0)$

Equation Form:

$x = 3, y = 0$

Step 7

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

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