Solve by Substitution 5x+4y=-14 , 3x+6y=6

$5 x + 4 y = - 14$ , $3 x + 6 y = 6$

Step 1

Solve for $x$ in $5 x + 4 y = - 14$ .

Subtract $4 y$ from both sides of the equation.

$5 x = - 14 - 4 y$

$3 x + 6 y = 6$

Divide each term in $5 x = - 14 - 4 y$ by $5$ and simplify.

Divide each term in $5 x = - 14 - 4 y$ by $5$ .

$\frac{5 x}{5} = \frac{- 14}{5} + \frac{- 4 y}{5}$

$3 x + 6 y = 6$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 14}{5} + \frac{- 4 y}{5}$

$3 x + 6 y = 6$

Divide $x$ by $1$ .

$x = \frac{- 14}{5} + \frac{- 4 y}{5}$

$3 x + 6 y = 6$

$x = \frac{- 14}{5} + \frac{- 4 y}{5}$

$3 x + 6 y = 6$

$x = \frac{- 14}{5} + \frac{- 4 y}{5}$

$3 x + 6 y = 6$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{14}{5} + \frac{- 4 y}{5}$

$3 x + 6 y = 6$

Move the negative in front of the fraction.

$x = - \frac{14}{5} - \frac{4 y}{5}$

$3 x + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$3 x + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$3 x + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$3 x + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$3 x + 6 y = 6$

Step 2

Replace all occurrences of $x$ with $- \frac{14}{5} - \frac{4 y}{5}$ in each equation.

Replace all occurrences of $x$ in $3 x + 6 y = 6$ with $- \frac{14}{5} - \frac{4 y}{5}$ .

$3 (- \frac{14}{5} - \frac{4 y}{5}) + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Simplify the left side.

Simplify $3 (- \frac{14}{5} - \frac{4 y}{5}) + 6 y$ .

Simplify each term.

Apply the distributive property.

$3 (- \frac{14}{5}) + 3 (- \frac{4 y}{5}) + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Multiply $3 (- \frac{14}{5})$ .

Multiply $- 1$ by $3$ .

$- 3 (\frac{14}{5}) + 3 (- \frac{4 y}{5}) + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Combine $- 3$ and $\frac{14}{5}$ .

$\frac{- 3 \cdot 14}{5} + 3 (- \frac{4 y}{5}) + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Multiply $- 3$ by $14$ .

$\frac{- 42}{5} + 3 (- \frac{4 y}{5}) + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$\frac{- 42}{5} + 3 (- \frac{4 y}{5}) + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Multiply $3 (- \frac{4 y}{5})$ .

Multiply $- 1$ by $3$ .

$\frac{- 42}{5} - 3 \frac{4 y}{5} + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Combine $- 3$ and $\frac{4 y}{5}$ .

$\frac{- 42}{5} + \frac{- 3 (4 y)}{5} + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Multiply $4$ by $- 3$ .

$\frac{- 42}{5} + \frac{- 12 y}{5} + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$\frac{- 42}{5} + \frac{- 12 y}{5} + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{42}{5} + \frac{- 12 y}{5} + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Move the negative in front of the fraction.

$- \frac{42}{5} - \frac{12 y}{5} + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$- \frac{42}{5} - \frac{12 y}{5} + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$- \frac{42}{5} - \frac{12 y}{5} + 6 y = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

To write $6 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{42}{5} - \frac{12 y}{5} + 6 y \cdot \frac{5}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Combine $6 y$ and $\frac{5}{5}$ .

$- \frac{42}{5} - \frac{12 y}{5} + \frac{6 y \cdot 5}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Combine the numerators over the common denominator.

$- \frac{42}{5} + \frac{- 12 y + 6 y \cdot 5}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Combine the numerators over the common denominator.

$\frac{- 42 - 12 y + 6 y \cdot 5}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Multiply $5$ by $6$ .

$\frac{- 42 - 12 y + 30 y}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Add $- 12 y$ and $30 y$ .

$\frac{- 42 + 18 y}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Factor $6$ out of $- 42 + 18 y$ .

Factor $6$ out of $- 42$ .

$\frac{6 (- 7) + 18 y}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Factor $6$ out of $18 y$ .

$\frac{6 (- 7) + 6 (3 y)}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Factor $6$ out of $6 (- 7) + 6 (3 y)$ .

$\frac{6 (- 7 + 3 y)}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$\frac{6 (- 7 + 3 y)}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{6 (- 1 \cdot 7 + 3 y)}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Factor $- 1$ out of $3 y$ .

$\frac{6 (- 1 \cdot 7 - (- 3 y))}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Factor $- 1$ out of $- 1 (7) - (- 3 y)$ .

$\frac{6 (- 1 (7 - 3 y))}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Move the negative in front of the fraction.

$- \frac{6 (7 - 3 y)}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$- \frac{6 (7 - 3 y)}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$- \frac{6 (7 - 3 y)}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$- \frac{6 (7 - 3 y)}{5} = 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Step 3

Solve for $y$ in $- \frac{6 (7 - 3 y)}{5} = 6$ .

Multiply both sides of the equation by $- \frac{5}{6}$ .

$- \frac{5}{6} \cdot (- \frac{6 (7 - 3 y)}{5}) = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{6} (- \frac{6 (7 - 3 y)}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{- 5}{6} \cdot (- \frac{6 (7 - 3 y)}{5}) = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Move the leading negative in $- \frac{6 (7 - 3 y)}{5}$ into the numerator.

$\frac{- 5}{6} \cdot \frac{- 6 (7 - 3 y)}{5} = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{6} \cdot \frac{- 6 (7 - 3 y)}{5} = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Cancel the common factor.

$\frac{5 \cdot - 1}{6} \cdot \frac{- 6 (7 - 3 y)}{5} = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Rewrite the expression.

$\frac{- 1}{6} \cdot (- 6 (7 - 3 y)) = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$\frac{- 1}{6} \cdot (- 6 (7 - 3 y)) = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Cancel the common factor of $6$ .

Factor $6$ out of $- 6 (7 - 3 y)$ .

$\frac{- 1}{6} \cdot (6 (- (7 - 3 y))) = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Cancel the common factor.

$\frac{- 1}{6} \cdot (6 (- (7 - 3 y))) = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Rewrite the expression.

$7 - 3 y = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$7 - 3 y = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (7 - 3 y) = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Multiply $7 - 3 y$ by $1$ .

$7 - 3 y = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$7 - 3 y = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$7 - 3 y = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$7 - 3 y = - \frac{5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Simplify the right side.

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$7 - 3 y = \frac{- 5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Cancel the common factor.

$7 - 3 y = \frac{- 5}{6} \cdot 6$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Rewrite the expression.

$7 - 3 y = - 5$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$7 - 3 y = - 5$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$7 - 3 y = - 5$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$7 - 3 y = - 5$

$x = - \frac{14}{5} - \frac{4 y}{5}$

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

Subtract $7$ from both sides of the equation.

$- 3 y = - 5 - 7$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Subtract $7$ from $- 5$ .

$- 3 y = - 12$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$- 3 y = - 12$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Divide each term in $- 3 y = - 12$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 12$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 12}{- 3}$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 12}{- 3}$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Divide $y$ by $1$ .

$y = \frac{- 12}{- 3}$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$y = \frac{- 12}{- 3}$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$y = \frac{- 12}{- 3}$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$y = 4$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$y = 4$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$y = 4$

$x = - \frac{14}{5} - \frac{4 y}{5}$

$y = 4$

$x = - \frac{14}{5} - \frac{4 y}{5}$

Step 4

Replace all occurrences of $y$ with $4$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{14}{5} - \frac{4 y}{5}$ with $4$ .

$x = - \frac{14}{5} - \frac{4 (4)}{5}$

$y = 4$

Simplify the right side.

Simplify $- \frac{14}{5} - \frac{4 (4)}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{- 14 - 4 \cdot 4}{5}$

$y = 4$

Simplify the expression.

Multiply $- 4$ by $4$ .

$x = \frac{- 14 - 16}{5}$

$y = 4$

Subtract $16$ from $- 14$ .

$x = \frac{- 30}{5}$

$y = 4$

Divide $- 30$ by $5$ .

$x = - 6$

$y = 4$

$x = - 6$

$y = 4$

$x = - 6$

$y = 4$

$x = - 6$

$y = 4$

$x = - 6$

$y = 4$

Step 5

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

$(- 6, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, 4)$

Equation Form:

$x = - 6, y = 4$

Step 7

Solve by Substitution 5x+4y=-14 , 3x+6y=6

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