Solve by Substitution -2x-4y=1 , 12y=-6x-3

$- 2 x - 4 y = 1$ , $12 y = - 6 x - 3$

Step 1

Divide each term in $12 y = - 6 x - 3$ by $12$ and simplify.

Divide each term in $12 y = - 6 x - 3$ by $12$ .

$\frac{12 y}{12} = \frac{- 6 x}{12} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 y}{12} = \frac{- 6 x}{12} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

Divide $y$ by $1$ .

$y = \frac{- 6 x}{12} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

$y = \frac{- 6 x}{12} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

$y = \frac{- 6 x}{12} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 6$ and $12$ .

Factor $6$ out of $- 6 x$ .

$y = \frac{6 (- x)}{12} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

Cancel the common factors.

Factor $6$ out of $12$ .

$y = \frac{6 (- x)}{6 (2)} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

Cancel the common factor.

$y = \frac{6 (- x)}{6 \cdot 2} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

Rewrite the expression.

$y = \frac{- x}{2} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

$y = \frac{- x}{2} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

$y = \frac{- x}{2} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{- 3}{12}$

$- 2 x - 4 y = 1$

Cancel the common factor of $- 3$ and $12$ .

Factor $3$ out of $- 3$ .

$y = - \frac{x}{2} + \frac{3 (- 1)}{12}$

$- 2 x - 4 y = 1$

Cancel the common factors.

Factor $3$ out of $12$ .

$y = - \frac{x}{2} + \frac{3 \cdot - 1}{3 \cdot 4}$

$- 2 x - 4 y = 1$

Cancel the common factor.

$y = - \frac{x}{2} + \frac{3 \cdot - 1}{3 \cdot 4}$

$- 2 x - 4 y = 1$

Rewrite the expression.

$y = - \frac{x}{2} + \frac{- 1}{4}$

$- 2 x - 4 y = 1$

$y = - \frac{x}{2} + \frac{- 1}{4}$

$- 2 x - 4 y = 1$

$y = - \frac{x}{2} + \frac{- 1}{4}$

$- 2 x - 4 y = 1$

Move the negative in front of the fraction.

$y = - \frac{x}{2} - \frac{1}{4}$

$- 2 x - 4 y = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$- 2 x - 4 y = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$- 2 x - 4 y = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$- 2 x - 4 y = 1$

Step 2

Replace all occurrences of $y$ with $- \frac{x}{2} - \frac{1}{4}$ in each equation.

Replace all occurrences of $y$ in $- 2 x - 4 y = 1$ with $- \frac{x}{2} - \frac{1}{4}$ .

$- 2 x - 4 (- \frac{x}{2} - \frac{1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Simplify the left side.

Simplify $- 2 x - 4 (- \frac{x}{2} - \frac{1}{4})$ .

Simplify each term.

Apply the distributive property.

$- 2 x - 4 (- \frac{x}{2}) - 4 (- \frac{1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$- 2 x - 4 \frac{- x}{2} - 4 (- \frac{1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Factor $2$ out of $- 4$ .

$- 2 x + 2 (- 2) (\frac{- x}{2}) - 4 (- \frac{1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Cancel the common factor.

$- 2 x + 2 \cdot (- 2 \frac{- x}{2}) - 4 (- \frac{1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Rewrite the expression.

$- 2 x - 2 (- x) - 4 (- \frac{1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$- 2 x - 2 (- x) - 4 (- \frac{1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Multiply $- 1$ by $- 2$ .

$- 2 x + 2 x - 4 (- \frac{1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$- 2 x + 2 x - 4 (\frac{- 1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Factor $4$ out of $- 4$ .

$- 2 x + 2 x + 4 (- 1) (\frac{- 1}{4}) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Cancel the common factor.

$- 2 x + 2 x + 4 \cdot (- 1 (\frac{- 1}{4})) = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Rewrite the expression.

$- 2 x + 2 x - 1 \cdot - 1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$- 2 x + 2 x - 1 \cdot - 1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Multiply $- 1$ by $- 1$ .

$- 2 x + 2 x + 1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$- 2 x + 2 x + 1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Simplify by adding terms.

Add $- 2 x$ and $2 x$ .

$0 + 1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Add $0$ and $1$ .

$1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

$1 = 1$

$y = - \frac{x}{2} - \frac{1}{4}$

Step 3

Remove any equations from the system that are always true.

$y = - \frac{x}{2} - \frac{1}{4}$

Step 4

Related Questions