Solve by Substitution 7x+2y=-19 , -x+2y=21

$7 x + 2 y = - 19$ , $- x + 2 y = 21$

Step 1

Solve for $x$ in $7 x + 2 y = - 19$ .

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

$7 x = - 19 - 2 y$

$- x + 2 y = 21$

Divide each term in $7 x = - 19 - 2 y$ by $7$ and simplify.

Divide each term in $7 x = - 19 - 2 y$ by $7$ .

$\frac{7 x}{7} = \frac{- 19}{7} + \frac{- 2 y}{7}$

$- x + 2 y = 21$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 19}{7} + \frac{- 2 y}{7}$

$- x + 2 y = 21$

Divide $x$ by $1$ .

$x = \frac{- 19}{7} + \frac{- 2 y}{7}$

$- x + 2 y = 21$

$x = \frac{- 19}{7} + \frac{- 2 y}{7}$

$- x + 2 y = 21$

$x = \frac{- 19}{7} + \frac{- 2 y}{7}$

$- x + 2 y = 21$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{19}{7} + \frac{- 2 y}{7}$

$- x + 2 y = 21$

Move the negative in front of the fraction.

$x = - \frac{19}{7} - \frac{2 y}{7}$

$- x + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$- x + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$- x + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$- x + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$- x + 2 y = 21$

Step 2

Replace all occurrences of $x$ with $- \frac{19}{7} - \frac{2 y}{7}$ in each equation.

Replace all occurrences of $x$ in $- x + 2 y = 21$ with $- \frac{19}{7} - \frac{2 y}{7}$ .

$- (- \frac{19}{7} - \frac{2 y}{7}) + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Simplify the left side.

Simplify $- (- \frac{19}{7} - \frac{2 y}{7}) + 2 y$ .

Simplify each term.

Apply the distributive property.

$\frac{19}{7} + \frac{2 y}{7} + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Multiply $- - \frac{19}{7}$ .

Multiply $- 1$ by $- 1$ .

$1 (\frac{19}{7}) + \frac{2 y}{7} + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Multiply $\frac{19}{7}$ by $1$ .

$\frac{19}{7} + \frac{2 y}{7} + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$\frac{19}{7} + \frac{2 y}{7} + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Multiply $- - \frac{2 y}{7}$ .

Multiply $- 1$ by $- 1$ .

$\frac{19}{7} + 1 (\frac{2 y}{7}) + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Multiply $\frac{2 y}{7}$ by $1$ .

$\frac{19}{7} + \frac{2 y}{7} + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$\frac{19}{7} + \frac{2 y}{7} + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$\frac{19}{7} + \frac{2 y}{7} + 2 y = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{19}{7} + \frac{2 y}{7} + 2 y \cdot \frac{7}{7} = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

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

$\frac{19}{7} + \frac{2 y}{7} + \frac{2 y \cdot 7}{7} = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Combine the numerators over the common denominator.

$\frac{19}{7} + \frac{2 y + 2 y \cdot 7}{7} = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Combine the numerators over the common denominator.

$\frac{19 + 2 y + 2 y \cdot 7}{7} = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Multiply $7$ by $2$ .

$\frac{19 + 2 y + 14 y}{7} = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Add $2 y$ and $14 y$ .

$\frac{19 + 16 y}{7} = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$\frac{19 + 16 y}{7} = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$\frac{19 + 16 y}{7} = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$\frac{19 + 16 y}{7} = 21$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Step 3

Solve for $y$ in $\frac{19 + 16 y}{7} = 21$ .

Multiply both sides by $7$ .

$\frac{19 + 16 y}{7} \cdot 7 = 21 \cdot 7$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Simplify.

Simplify the left side.

Simplify $\frac{19 + 16 y}{7} \cdot 7$ .

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{19 + 16 y}{7} \cdot 7 = 21 \cdot 7$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Rewrite the expression.

$19 + 16 y = 21 \cdot 7$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$19 + 16 y = 21 \cdot 7$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Reorder $19$ and $16 y$ .

$16 y + 19 = 21 \cdot 7$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$16 y + 19 = 21 \cdot 7$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$16 y + 19 = 21 \cdot 7$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Simplify the right side.

Multiply $21$ by $7$ .

$16 y + 19 = 147$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$16 y + 19 = 147$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$16 y + 19 = 147$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Solve for $y$ .

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

Subtract $19$ from both sides of the equation.

$16 y = 147 - 19$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Subtract $19$ from $147$ .

$16 y = 128$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$16 y = 128$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Divide each term in $16 y = 128$ by $16$ and simplify.

Divide each term in $16 y = 128$ by $16$ .

$\frac{16 y}{16} = \frac{128}{16}$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 y}{16} = \frac{128}{16}$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Divide $y$ by $1$ .

$y = \frac{128}{16}$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$y = \frac{128}{16}$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$y = \frac{128}{16}$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Simplify the right side.

Divide $128$ by $16$ .

$y = 8$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$y = 8$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$y = 8$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$y = 8$

$x = - \frac{19}{7} - \frac{2 y}{7}$

$y = 8$

$x = - \frac{19}{7} - \frac{2 y}{7}$

Step 4

Replace all occurrences of $y$ with $8$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{19}{7} - \frac{2 y}{7}$ with $8$ .

$x = - \frac{19}{7} - \frac{2 (8)}{7}$

$y = 8$

Simplify the right side.

Simplify $- \frac{19}{7} - \frac{2 (8)}{7}$ .

Combine the numerators over the common denominator.

$x = \frac{- 19 - 2 \cdot 8}{7}$

$y = 8$

Simplify the expression.

Multiply $- 2$ by $8$ .

$x = \frac{- 19 - 16}{7}$

$y = 8$

Subtract $16$ from $- 19$ .

$x = \frac{- 35}{7}$

$y = 8$

Divide $- 35$ by $7$ .

$x = - 5$

$y = 8$

$x = - 5$

$y = 8$

$x = - 5$

$y = 8$

$x = - 5$

$y = 8$

$x = - 5$

$y = 8$

Step 5

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

$(- 5, 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 5, 8)$

Equation Form:

$x = - 5, y = 8$

Step 7

Solve by Substitution 7x+2y=-19 , -x+2y=21

Related Questions

Support LCMGCF.com by disabling your adblocker.