Solve by Substitution -3x-4y=2 , 3x+3y=-3

$- 3 x - 4 y = 2$ , $3 x + 3 y = - 3$

Step 1

Solve for $x$ in $- 3 x - 4 y = 2$ .

Add $4 y$ to both sides of the equation.

$- 3 x = 2 + 4 y$

$3 x + 3 y = - 3$

Divide each term in $- 3 x = 2 + 4 y$ by $- 3$ and simplify.

Divide each term in $- 3 x = 2 + 4 y$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{2}{- 3} + \frac{4 y}{- 3}$

$3 x + 3 y = - 3$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{2}{- 3} + \frac{4 y}{- 3}$

$3 x + 3 y = - 3$

Divide $x$ by $1$ .

$x = \frac{2}{- 3} + \frac{4 y}{- 3}$

$3 x + 3 y = - 3$

$x = \frac{2}{- 3} + \frac{4 y}{- 3}$

$3 x + 3 y = - 3$

$x = \frac{2}{- 3} + \frac{4 y}{- 3}$

$3 x + 3 y = - 3$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{2}{3} + \frac{4 y}{- 3}$

$3 x + 3 y = - 3$

Move the negative in front of the fraction.

$x = - \frac{2}{3} - \frac{4 y}{3}$

$3 x + 3 y = - 3$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$3 x + 3 y = - 3$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$3 x + 3 y = - 3$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$3 x + 3 y = - 3$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$3 x + 3 y = - 3$

Step 2

Replace all occurrences of $x$ with $- \frac{2}{3} - \frac{4 y}{3}$ in each equation.

Replace all occurrences of $x$ in $3 x + 3 y = - 3$ with $- \frac{2}{3} - \frac{4 y}{3}$ .

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Cancel the common factor.

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Rewrite the expression.

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4 y}{3}$ into the numerator.

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Cancel the common factor.

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Rewrite the expression.

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

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

$- 2 - y = - 3$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$- 2 - y = - 3$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$- 2 - y = - 3$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$- 2 - y = - 3$

$x = - \frac{2}{3} - \frac{4 y}{3}$

Step 3

Solve for $y$ in $- 2 - y = - 3$ .

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

Add $2$ to both sides of the equation.

$- y = - 3 + 2$

$x = - \frac{2}{3} - \frac{4 y}{3}$

Add $- 3$ and $2$ .

$- y = - 1$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$- y = - 1$

$x = - \frac{2}{3} - \frac{4 y}{3}$

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

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

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Simplify the left side.

Dividing two negative values results in a positive value.

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Divide $y$ by $1$ .

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

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

$x = - \frac{2}{3} - \frac{4 y}{3}$

Simplify the right side.

Divide $- 1$ by $- 1$ .

$y = 1$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$y = 1$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$y = 1$

$x = - \frac{2}{3} - \frac{4 y}{3}$

$y = 1$

$x = - \frac{2}{3} - \frac{4 y}{3}$

Step 4

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

Replace all occurrences of $y$ in $x = - \frac{2}{3} - \frac{4 y}{3}$ with $1$ .

$x = - \frac{2}{3} - \frac{4 (1)}{3}$

$y = 1$

Simplify the right side.

Simplify $- \frac{2}{3} - \frac{4 (1)}{3}$ .

Combine the numerators over the common denominator.

$x = \frac{- 2 - 4 \cdot 1}{3}$

$y = 1$

Simplify the expression.

Multiply $- 4$ by $1$ .

$x = \frac{- 2 - 4}{3}$

$y = 1$

Subtract $4$ from $- 2$ .

$x = \frac{- 6}{3}$

$y = 1$

Divide $- 6$ by $3$ .

$x = - 2$

$y = 1$

$x = - 2$

$y = 1$

$x = - 2$

$y = 1$

$x = - 2$

$y = 1$

$x = - 2$

$y = 1$

Step 5

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

$(- 2, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, 1)$

Equation Form:

$x = - 2, y = 1$

Step 7

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