Solve by Substitution 2x+3y=0 , x+2y=-1

$2 x + 3 y = 0$ , $x + 2 y = - 1$

Step 1

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

$x = - 1 - 2 y$

$2 x + 3 y = 0$

Step 2

Replace all occurrences of $x$ with $- 1 - 2 y$ in each equation.

Replace all occurrences of $x$ in $2 x + 3 y = 0$ with $- 1 - 2 y$ .

$2 (- 1 - 2 y) + 3 y = 0$

$x = - 1 - 2 y$

Simplify the left side.

Simplify $2 (- 1 - 2 y) + 3 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 1 + 2 (- 2 y) + 3 y = 0$

$x = - 1 - 2 y$

Multiply $2$ by $- 1$ .

$- 2 + 2 (- 2 y) + 3 y = 0$

$x = - 1 - 2 y$

Multiply $- 2$ by $2$ .

$- 2 - 4 y + 3 y = 0$

$x = - 1 - 2 y$

$- 2 - 4 y + 3 y = 0$

$x = - 1 - 2 y$

Add $- 4 y$ and $3 y$ .

$- 2 - y = 0$

$x = - 1 - 2 y$

$- 2 - y = 0$

$x = - 1 - 2 y$

$- 2 - y = 0$

$x = - 1 - 2 y$

$- 2 - y = 0$

$x = - 1 - 2 y$

Step 3

Solve for $y$ in $- 2 - y = 0$ .

Add $2$ to both sides of the equation.

$- y = 2$

$x = - 1 - 2 y$

Divide each term in $- y = 2$ by $- 1$ and simplify.

Divide each term in $- y = 2$ by $- 1$ .

$\frac{- y}{- 1} = \frac{2}{- 1}$

$x = - 1 - 2 y$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{2}{- 1}$

$x = - 1 - 2 y$

Divide $y$ by $1$ .

$y = \frac{2}{- 1}$

$x = - 1 - 2 y$

$y = \frac{2}{- 1}$

$x = - 1 - 2 y$

Simplify the right side.

Divide $2$ by $- 1$ .

$y = - 2$

$x = - 1 - 2 y$

$y = - 2$

$x = - 1 - 2 y$

$y = - 2$

$x = - 1 - 2 y$

$y = - 2$

$x = - 1 - 2 y$

Step 4

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

Replace all occurrences of $y$ in $x = - 1 - 2 y$ with $- 2$ .

$x = - 1 - 2 \cdot - 2$

$y = - 2$

Simplify the right side.

Simplify $- 1 - 2 \cdot - 2$ .

Multiply $- 2$ by $- 2$ .

$x = - 1 + 4$

$y = - 2$

Add $- 1$ and $4$ .

$x = 3$

$y = - 2$

$x = 3$

$y = - 2$

$x = 3$

$y = - 2$

$x = 3$

$y = - 2$

Step 5

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

$(3, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, - 2)$

Equation Form:

$x = 3, y = - 2$

Step 7

Solve by Substitution 2x+3y=0 , x+2y=-1

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