Solve by Substitution -7x-2y=-13 and x-2y=11

$- 7 x - 2 y = - 13$ and $x - 2 y = 11$

Step 1

Add $2 y$ to both sides of the equation.

$x = 11 + 2 y$

$- 7 x - 2 y = - 13$

Step 2

Replace all occurrences of $x$ with $11 + 2 y$ in each equation.

Replace all occurrences of $x$ in $- 7 x - 2 y = - 13$ with $11 + 2 y$ .

$- 7 (11 + 2 y) - 2 y = - 13$

$x = 11 + 2 y$

Simplify the left side.

Simplify $- 7 (11 + 2 y) - 2 y$ .

Simplify each term.

Apply the distributive property.

$- 7 \cdot 11 - 7 (2 y) - 2 y = - 13$

$x = 11 + 2 y$

Multiply $- 7$ by $11$ .

$- 77 - 7 (2 y) - 2 y = - 13$

$x = 11 + 2 y$

Multiply $2$ by $- 7$ .

$- 77 - 14 y - 2 y = - 13$

$x = 11 + 2 y$

$- 77 - 14 y - 2 y = - 13$

$x = 11 + 2 y$

Subtract $2 y$ from $- 14 y$ .

$- 77 - 16 y = - 13$

$x = 11 + 2 y$

$- 77 - 16 y = - 13$

$x = 11 + 2 y$

$- 77 - 16 y = - 13$

$x = 11 + 2 y$

$- 77 - 16 y = - 13$

$x = 11 + 2 y$

Step 3

Solve for $y$ in $- 77 - 16 y = - 13$ .

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

Add $77$ to both sides of the equation.

$- 16 y = - 13 + 77$

$x = 11 + 2 y$

Add $- 13$ and $77$ .

$- 16 y = 64$

$x = 11 + 2 y$

$- 16 y = 64$

$x = 11 + 2 y$

Divide each term in $- 16 y = 64$ by $- 16$ and simplify.

Divide each term in $- 16 y = 64$ by $- 16$ .

$\frac{- 16 y}{- 16} = \frac{64}{- 16}$

$x = 11 + 2 y$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 y}{- 16} = \frac{64}{- 16}$

$x = 11 + 2 y$

Divide $y$ by $1$ .

$y = \frac{64}{- 16}$

$x = 11 + 2 y$

$y = \frac{64}{- 16}$

$x = 11 + 2 y$

$y = \frac{64}{- 16}$

$x = 11 + 2 y$

Simplify the right side.

Divide $64$ by $- 16$ .

$y = - 4$

$x = 11 + 2 y$

$y = - 4$

$x = 11 + 2 y$

$y = - 4$

$x = 11 + 2 y$

$y = - 4$

$x = 11 + 2 y$

Step 4

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

Replace all occurrences of $y$ in $x = 11 + 2 y$ with $- 4$ .

$x = 11 + 2 (- 4)$

$y = - 4$

Simplify the right side.

Simplify $11 + 2 (- 4)$ .

Multiply $2$ by $- 4$ .

$x = 11 - 8$

$y = - 4$

Subtract $8$ from $11$ .

$x = 3$

$y = - 4$

$x = 3$

$y = - 4$

$x = 3$

$y = - 4$

$x = 3$

$y = - 4$

Step 5

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

$(3, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, - 4)$

Equation Form:

$x = 3, y = - 4$

Step 7

Solve by Substitution -7x-2y=-13 and x-2y=11

Related Questions

Support LCMGCF.com by disabling your adblocker.