Solve by Substitution 7x+2y=-1 , 3x-4y=19

$7 x + 2 y = - 1$ , $3 x - 4 y = 19$

Step 1

Solve for $x$ in $7 x + 2 y = - 1$ .

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

$7 x = - 1 - 2 y$

$3 x - 4 y = 19$

Divide each term in $7 x = - 1 - 2 y$ by $7$ and simplify.

Divide each term in $7 x = - 1 - 2 y$ by $7$ .

$\frac{7 x}{7} = \frac{- 1}{7} + \frac{- 2 y}{7}$

$3 x - 4 y = 19$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 1}{7} + \frac{- 2 y}{7}$

$3 x - 4 y = 19$

Divide $x$ by $1$ .

$x = \frac{- 1}{7} + \frac{- 2 y}{7}$

$3 x - 4 y = 19$

$x = \frac{- 1}{7} + \frac{- 2 y}{7}$

$3 x - 4 y = 19$

$x = \frac{- 1}{7} + \frac{- 2 y}{7}$

$3 x - 4 y = 19$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{1}{7} + \frac{- 2 y}{7}$

$3 x - 4 y = 19$

Move the negative in front of the fraction.

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 x - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 x - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 x - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 x - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 x - 4 y = 19$

Step 2

Replace all occurrences of $x$ with $- \frac{1}{7} - \frac{2 y}{7}$ in each equation.

Replace all occurrences of $x$ in $3 x - 4 y = 19$ with $- \frac{1}{7} - \frac{2 y}{7}$ .

$3 (- \frac{1}{7} - \frac{2 y}{7}) - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Simplify the left side.

Simplify $3 (- \frac{1}{7} - \frac{2 y}{7}) - 4 y$ .

Simplify each term.

Apply the distributive property.

$3 (- \frac{1}{7}) + 3 (- \frac{2 y}{7}) - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Multiply $3 (- \frac{1}{7})$ .

Multiply $- 1$ by $3$ .

$- 3 (\frac{1}{7}) + 3 (- \frac{2 y}{7}) - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Combine $- 3$ and $\frac{1}{7}$ .

$\frac{- 3}{7} + 3 (- \frac{2 y}{7}) - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$\frac{- 3}{7} + 3 (- \frac{2 y}{7}) - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Multiply $3 (- \frac{2 y}{7})$ .

Multiply $- 1$ by $3$ .

$\frac{- 3}{7} - 3 \frac{2 y}{7} - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Combine $- 3$ and $\frac{2 y}{7}$ .

$\frac{- 3}{7} + \frac{- 3 (2 y)}{7} - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Multiply $2$ by $- 3$ .

$\frac{- 3}{7} + \frac{- 6 y}{7} - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$\frac{- 3}{7} + \frac{- 6 y}{7} - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{3}{7} + \frac{- 6 y}{7} - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Move the negative in front of the fraction.

$- \frac{3}{7} - \frac{6 y}{7} - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$- \frac{3}{7} - \frac{6 y}{7} - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$- \frac{3}{7} - \frac{6 y}{7} - 4 y = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

To write $- 4 y$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{3}{7} - \frac{6 y}{7} - 4 y \cdot \frac{7}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Combine $- 4 y$ and $\frac{7}{7}$ .

$- \frac{3}{7} - \frac{6 y}{7} + \frac{- 4 y \cdot 7}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Combine the numerators over the common denominator.

$- \frac{3}{7} + \frac{- 6 y - 4 y \cdot 7}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Combine the numerators over the common denominator.

$\frac{- 3 - 6 y - 4 y \cdot 7}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Multiply $7$ by $- 4$ .

$\frac{- 3 - 6 y - 28 y}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Subtract $28 y$ from $- 6 y$ .

$\frac{- 3 - 34 y}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- 1 \cdot 3 - 34 y}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Factor $- 1$ out of $- 34 y$ .

$\frac{- 1 \cdot 3 - (34 y)}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Factor $- 1$ out of $- 1 (3) - (34 y)$ .

$\frac{- 1 (3 + 34 y)}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Move the negative in front of the fraction.

$- \frac{3 + 34 y}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$- \frac{3 + 34 y}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$- \frac{3 + 34 y}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$- \frac{3 + 34 y}{7} = 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Step 3

Solve for $y$ in $- \frac{3 + 34 y}{7} = 19$ .

Multiply both sides of the equation by $- 7$ .

$- 7 (- \frac{3 + 34 y}{7}) = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 7 (- \frac{3 + 34 y}{7})$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{3 + 34 y}{7}$ into the numerator.

$- 7 \frac{- (3 + 34 y)}{7} = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Factor $7$ out of $- 7$ .

$7 (- 1) (\frac{- (3 + 34 y)}{7}) = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Cancel the common factor.

$7 \cdot (- 1 \frac{- (3 + 34 y)}{7}) = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Rewrite the expression.

$3 + 34 y = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 + 34 y = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (3 + 34 y) = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Multiply $3 + 34 y$ by $1$ .

$3 + 34 y = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 + 34 y = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 + 34 y = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 + 34 y = - 7 \cdot 19$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Simplify the right side.

Multiply $- 7$ by $19$ .

$3 + 34 y = - 133$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 + 34 y = - 133$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$3 + 34 y = - 133$

$x = - \frac{1}{7} - \frac{2 y}{7}$

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

Subtract $3$ from both sides of the equation.

$34 y = - 133 - 3$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Subtract $3$ from $- 133$ .

$34 y = - 136$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$34 y = - 136$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Divide each term in $34 y = - 136$ by $34$ and simplify.

Divide each term in $34 y = - 136$ by $34$ .

$\frac{34 y}{34} = \frac{- 136}{34}$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Simplify the left side.

Cancel the common factor of $34$ .

Cancel the common factor.

$\frac{34 y}{34} = \frac{- 136}{34}$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Divide $y$ by $1$ .

$y = \frac{- 136}{34}$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$y = \frac{- 136}{34}$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$y = \frac{- 136}{34}$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Simplify the right side.

Divide $- 136$ by $34$ .

$y = - 4$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$y = - 4$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$y = - 4$

$x = - \frac{1}{7} - \frac{2 y}{7}$

$y = - 4$

$x = - \frac{1}{7} - \frac{2 y}{7}$

Step 4

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

Replace all occurrences of $y$ in $x = - \frac{1}{7} - \frac{2 y}{7}$ with $- 4$ .

$x = - \frac{1}{7} - \frac{2 (- 4)}{7}$

$y = - 4$

Simplify the right side.

Simplify $- \frac{1}{7} - \frac{2 (- 4)}{7}$ .

Combine the numerators over the common denominator.

$x = \frac{- 1 - 2 \cdot - 4}{7}$

$y = - 4$

Simplify the expression.

Multiply $- 2$ by $- 4$ .

$x = \frac{- 1 + 8}{7}$

$y = - 4$

Add $- 1$ and $8$ .

$x = \frac{7}{7}$

$y = - 4$

Divide $7$ by $7$ .

$x = 1$

$y = - 4$

$x = 1$

$y = - 4$

$x = 1$

$y = - 4$

$x = 1$

$y = - 4$

$x = 1$

$y = - 4$

Step 5

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

$(1, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, - 4)$

Equation Form:

$x = 1, y = - 4$

Step 7

Solve by Substitution 7x+2y=-1 , 3x-4y=19

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