Solve the System of Equations x+2y=21 and -2x-y=-12

$x + 2 y = 21$ and $- 2 x - y = - 12$

Step 1

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

$x = 21 - 2 y$

$- 2 x - y = - 12$

Step 2

Replace all occurrences of $x$ with $21 - 2 y$ in each equation.

Replace all occurrences of $x$ in $- 2 x - y = - 12$ with $21 - 2 y$ .

$- 2 (21 - 2 y) - y = - 12$

$x = 21 - 2 y$

Simplify the left side.

Simplify $- 2 (21 - 2 y) - y$ .

Simplify each term.

Apply the distributive property.

$- 2 \cdot 21 - 2 (- 2 y) - y = - 12$

$x = 21 - 2 y$

Multiply $- 2$ by $21$ .

$- 42 - 2 (- 2 y) - y = - 12$

$x = 21 - 2 y$

Multiply $- 2$ by $- 2$ .

$- 42 + 4 y - y = - 12$

$x = 21 - 2 y$

$- 42 + 4 y - y = - 12$

$x = 21 - 2 y$

Subtract $y$ from $4 y$ .

$- 42 + 3 y = - 12$

$x = 21 - 2 y$

$- 42 + 3 y = - 12$

$x = 21 - 2 y$

$- 42 + 3 y = - 12$

$x = 21 - 2 y$

$- 42 + 3 y = - 12$

$x = 21 - 2 y$

Step 3

Solve for $y$ in $- 42 + 3 y = - 12$ .

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

Add $42$ to both sides of the equation.

$3 y = - 12 + 42$

$x = 21 - 2 y$

Add $- 12$ and $42$ .

$3 y = 30$

$x = 21 - 2 y$

$3 y = 30$

$x = 21 - 2 y$

Divide each term in $3 y = 30$ by $3$ and simplify.

Divide each term in $3 y = 30$ by $3$ .

$\frac{3 y}{3} = \frac{30}{3}$

$x = 21 - 2 y$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{30}{3}$

$x = 21 - 2 y$

Divide $y$ by $1$ .

$y = \frac{30}{3}$

$x = 21 - 2 y$

$y = \frac{30}{3}$

$x = 21 - 2 y$

$y = \frac{30}{3}$

$x = 21 - 2 y$

Simplify the right side.

Divide $30$ by $3$ .

$y = 10$

$x = 21 - 2 y$

$y = 10$

$x = 21 - 2 y$

$y = 10$

$x = 21 - 2 y$

$y = 10$

$x = 21 - 2 y$

Step 4

Replace all occurrences of $y$ with $10$ in each equation.

Replace all occurrences of $y$ in $x = 21 - 2 y$ with $10$ .

$x = 21 - 2 \cdot 10$

$y = 10$

Simplify the right side.

Simplify $21 - 2 \cdot 10$ .

Multiply $- 2$ by $10$ .

$x = 21 - 20$

$y = 10$

Subtract $20$ from $21$ .

$x = 1$

$y = 10$

$x = 1$

$y = 10$

$x = 1$

$y = 10$

$x = 1$

$y = 10$

Step 5

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

$(1, 10)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 10)$

Equation Form:

$x = 1, y = 10$

Step 7

Solve the System of Equations x+2y=21 and -2x-y=-12

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