Solve the System of Equations 2x-y=11 x+3y=-5

$2 x - y = 11$ $x + 3 y = - 5$

Step 1

Subtract $3 y$ from both sides of the equation.

$x = - 5 - 3 y$

$2 x - y = 11$

Step 2

Replace all occurrences of $x$ with $- 5 - 3 y$ in each equation.

Replace all occurrences of $x$ in $2 x - y = 11$ with $- 5 - 3 y$ .

$2 (- 5 - 3 y) - y = 11$

$x = - 5 - 3 y$

Simplify the left side.

Simplify $2 (- 5 - 3 y) - y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 5 + 2 (- 3 y) - y = 11$

$x = - 5 - 3 y$

Multiply $2$ by $- 5$ .

$- 10 + 2 (- 3 y) - y = 11$

$x = - 5 - 3 y$

Multiply $- 3$ by $2$ .

$- 10 - 6 y - y = 11$

$x = - 5 - 3 y$

$- 10 - 6 y - y = 11$

$x = - 5 - 3 y$

Subtract $y$ from $- 6 y$ .

$- 10 - 7 y = 11$

$x = - 5 - 3 y$

$- 10 - 7 y = 11$

$x = - 5 - 3 y$

$- 10 - 7 y = 11$

$x = - 5 - 3 y$

$- 10 - 7 y = 11$

$x = - 5 - 3 y$

Step 3

Solve for $y$ in $- 10 - 7 y = 11$ .

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

Add $10$ to both sides of the equation.

$- 7 y = 11 + 10$

$x = - 5 - 3 y$

Add $11$ and $10$ .

$- 7 y = 21$

$x = - 5 - 3 y$

$- 7 y = 21$

$x = - 5 - 3 y$

Divide each term in $- 7 y = 21$ by $- 7$ and simplify.

Divide each term in $- 7 y = 21$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{21}{- 7}$

$x = - 5 - 3 y$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{21}{- 7}$

$x = - 5 - 3 y$

Divide $y$ by $1$ .

$y = \frac{21}{- 7}$

$x = - 5 - 3 y$

$y = \frac{21}{- 7}$

$x = - 5 - 3 y$

$y = \frac{21}{- 7}$

$x = - 5 - 3 y$

Simplify the right side.

Divide $21$ by $- 7$ .

$y = - 3$

$x = - 5 - 3 y$

$y = - 3$

$x = - 5 - 3 y$

$y = - 3$

$x = - 5 - 3 y$

$y = - 3$

$x = - 5 - 3 y$

Step 4

Replace all occurrences of $y$ with $- 3$ in each equation.

Replace all occurrences of $y$ in $x = - 5 - 3 y$ with $- 3$ .

$x = - 5 - 3 \cdot - 3$

$y = - 3$

Simplify the right side.

Simplify $- 5 - 3 \cdot - 3$ .

Multiply $- 3$ by $- 3$ .

$x = - 5 + 9$

$y = - 3$

Add $- 5$ and $9$ .

$x = 4$

$y = - 3$

$x = 4$

$y = - 3$

$x = 4$

$y = - 3$

$x = 4$

$y = - 3$

Step 5

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

$(4, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, - 3)$

Equation Form:

$x = 4, y = - 3$

Step 7

Solve the System of Equations 2x-y=11 x+3y=-5

Related Questions

Support LCMGCF.com by disabling your adblocker.