Solve the System of Equations 2x+4y=12 -5x-10y=-30

$2 x + 4 y = 12$ $- 5 x - 10 y = - 30$

Step 1

Solve for $x$ in $2 x + 4 y = 12$ .

Subtract $4 y$ from both sides of the equation.

$2 x = 12 - 4 y$

$- 5 x - 10 y = - 30$

Divide each term in $2 x = 12 - 4 y$ by $2$ and simplify.

Divide each term in $2 x = 12 - 4 y$ by $2$ .

$\frac{2 x}{2} = \frac{12}{2} + \frac{- 4 y}{2}$

$- 5 x - 10 y = - 30$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{12}{2} + \frac{- 4 y}{2}$

$- 5 x - 10 y = - 30$

Divide $x$ by $1$ .

$x = \frac{12}{2} + \frac{- 4 y}{2}$

$- 5 x - 10 y = - 30$

$x = \frac{12}{2} + \frac{- 4 y}{2}$

$- 5 x - 10 y = - 30$

$x = \frac{12}{2} + \frac{- 4 y}{2}$

$- 5 x - 10 y = - 30$

Simplify the right side.

Simplify each term.

Divide $12$ by $2$ .

$x = 6 + \frac{- 4 y}{2}$

$- 5 x - 10 y = - 30$

Cancel the common factor of $- 4$ and $2$ .

Factor $2$ out of $- 4 y$ .

$x = 6 + \frac{2 (- 2 y)}{2}$

$- 5 x - 10 y = - 30$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = 6 + \frac{2 (- 2 y)}{2 (1)}$

$- 5 x - 10 y = - 30$

Cancel the common factor.

$x = 6 + \frac{2 (- 2 y)}{2 \cdot 1}$

$- 5 x - 10 y = - 30$

Rewrite the expression.

$x = 6 + \frac{- 2 y}{1}$

$- 5 x - 10 y = - 30$

Divide $- 2 y$ by $1$ .

$x = 6 - 2 y$

$- 5 x - 10 y = - 30$

$x = 6 - 2 y$

$- 5 x - 10 y = - 30$

$x = 6 - 2 y$

$- 5 x - 10 y = - 30$

$x = 6 - 2 y$

$- 5 x - 10 y = - 30$

$x = 6 - 2 y$

$- 5 x - 10 y = - 30$

$x = 6 - 2 y$

$- 5 x - 10 y = - 30$

$x = 6 - 2 y$

$- 5 x - 10 y = - 30$

Step 2

Replace all occurrences of $x$ with $6 - 2 y$ in each equation.

Replace all occurrences of $x$ in $- 5 x - 10 y = - 30$ with $6 - 2 y$ .

$- 5 (6 - 2 y) - 10 y = - 30$

$x = 6 - 2 y$

Simplify the left side.

Simplify $- 5 (6 - 2 y) - 10 y$ .

Simplify each term.

Apply the distributive property.

$- 5 \cdot 6 - 5 (- 2 y) - 10 y = - 30$

$x = 6 - 2 y$

Multiply $- 5$ by $6$ .

$- 30 - 5 (- 2 y) - 10 y = - 30$

$x = 6 - 2 y$

Multiply $- 2$ by $- 5$ .

$- 30 + 10 y - 10 y = - 30$

$x = 6 - 2 y$

$- 30 + 10 y - 10 y = - 30$

$x = 6 - 2 y$

Combine the opposite terms in $- 30 + 10 y - 10 y$ .

Subtract $10 y$ from $10 y$ .

$- 30 + 0 = - 30$

$x = 6 - 2 y$

Add $- 30$ and $0$ .

$- 30 = - 30$

$x = 6 - 2 y$

$- 30 = - 30$

$x = 6 - 2 y$

$- 30 = - 30$

$x = 6 - 2 y$

$- 30 = - 30$

$x = 6 - 2 y$

$- 30 = - 30$

$x = 6 - 2 y$

Step 3

Remove any equations from the system that are always true.

$x = 6 - 2 y$

Step 4

Solve the System of Equations 2x+4y=12 -5x-10y=-30

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