Solve by Addition/Elimination 1/4x+1/3y=1/12 1/4(-x+y)=-5/4

$\frac{1}{4} x + \frac{1}{3} y = \frac{1}{12}$ $\frac{1}{4} (- x + y) = - \frac{5}{4}$

Step 1

Multiply each term in $\frac{1}{4} x + \frac{1}{3} y = \frac{1}{12}$ by $12$ to eliminate the fractions.

Multiply each term in $\frac{1}{4} x + \frac{1}{3} y = \frac{1}{12}$ by $12$ .

$\frac{1}{4} x \cdot 12 + \frac{1}{3} y \cdot 12 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Simplify the left side.

Simplify each term.

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} \cdot 12 + \frac{1}{3} y \cdot 12 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$\frac{x}{4} \cdot (4 (3)) + \frac{1}{3} y \cdot 12 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Cancel the common factor.

$\frac{x}{4} \cdot (4 \cdot 3) + \frac{1}{3} y \cdot 12 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Rewrite the expression.

$x \cdot 3 + \frac{1}{3} y \cdot 12 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

$x \cdot 3 + \frac{1}{3} y \cdot 12 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Move $3$ to the left of $x$ .

$3 \cdot x + \frac{1}{3} y \cdot 12 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Combine $\frac{1}{3}$ and $y$ .

$3 x + \frac{y}{3} \cdot 12 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$3 x + \frac{y}{3} \cdot (3 (4)) = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Cancel the common factor.

$3 x + \frac{y}{3} \cdot (3 \cdot 4) = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Rewrite the expression.

$3 x + y \cdot 4 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

$3 x + y \cdot 4 = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Move $4$ to the left of $y$ .

$3 x + 4 y = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

$3 x + 4 y = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

$3 x + 4 y = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Simplify the right side.

Cancel the common factor of $12$ .

Cancel the common factor.

$3 x + 4 y = \frac{1}{12} \cdot 12$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Rewrite the expression.

$3 x + 4 y = 1$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

$3 x + 4 y = 1$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

$3 x + 4 y = 1$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

$3 x + 4 y = 1$

$\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$

Step 2

Multiply each term in $\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$ by $4$ to eliminate the fractions.

Multiply each term in $\frac{1}{4} \cdot (- x + y) = - \frac{5}{4}$ by $4$ .

$\frac{1}{4} \cdot (- x + y) \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Simplify the left side.

Apply the distributive property.

$(\frac{1}{4} \cdot (- x) + \frac{1}{4} y) \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Combine $\frac{1}{4}$ and $x$ .

$(- \frac{x}{4} + \frac{1}{4} y) \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Combine $\frac{1}{4}$ and $y$ .

$(- \frac{x}{4} + \frac{y}{4}) \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Apply the distributive property.

$- \frac{x}{4} \cdot 4 + \frac{y}{4} \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Cancel the common factor of $4$ .

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

$\frac{- x}{4} \cdot 4 + \frac{y}{4} \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Cancel the common factor.

$\frac{- x}{4} \cdot 4 + \frac{y}{4} \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Rewrite the expression.

$- x + \frac{y}{4} \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

$- x + \frac{y}{4} \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Cancel the common factor of $4$ .

Cancel the common factor.

$- x + \frac{y}{4} \cdot 4 = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Rewrite the expression.

$- x + y = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

$- x + y = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

$- x + y = - \frac{5}{4} \cdot 4$

$3 x + 4 y = 1$

Simplify the right side.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$- x + y = \frac{- 5}{4} \cdot 4$

$3 x + 4 y = 1$

Cancel the common factor.

$- x + y = \frac{- 5}{4} \cdot 4$

$3 x + 4 y = 1$

Rewrite the expression.

$- x + y = - 5$

$3 x + 4 y = 1$

$- x + y = - 5$

$3 x + 4 y = 1$

$- x + y = - 5$

$3 x + 4 y = 1$

$- x + y = - 5$

$3 x + 4 y = 1$

Step 3

Multiply each equation by the value that makes the coefficients of $x$ opposite.

$3 x + 4 y = 1$

$(3) \cdot (- x + y) = (3) (- 5)$

Step 4

Simplify.

Simplify the left side.

Simplify $(3) \cdot (- x + y)$ .

Apply the distributive property.

$3 x + 4 y = 1$

$3 (- x) + 3 y = (3) (- 5)$

Multiply $- 1$ by $3$ .

$3 x + 4 y = 1$

$- 3 x + 3 y = (3) (- 5)$

$3 x + 4 y = 1$

$- 3 x + 3 y = (3) (- 5)$

$3 x + 4 y = 1$

$- 3 x + 3 y = (3) (- 5)$

Simplify the right side.

Multiply $3$ by $- 5$ .

$3 x + 4 y = 1$

$- 3 x + 3 y = - 15$

$3 x + 4 y = 1$

$- 3 x + 3 y = - 15$

$3 x + 4 y = 1$

$- 3 x + 3 y = - 15$

Step 5

Add the two equations together to eliminate $x$ from the system.

				$3$	$x$	$+$	$4$	$y$	$=$			$1$
$+$			$-$	$3$	$x$	$+$	$3$	$y$	$=$	$-$	$1$	$5$
							$7$	$y$	$=$	$-$	$1$	$4$

Step 6

Divide each term in $7 y = - 14$ by $7$ and simplify.

Divide each term in $7 y = - 14$ by $7$ .

$\frac{7 y}{7} = \frac{- 14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 14}{7}$

Divide $y$ by $1$ .

$y = \frac{- 14}{7}$

$y = \frac{- 14}{7}$

$y = \frac{- 14}{7}$

Simplify the right side.

Divide $- 14$ by $7$ .

$y = - 2$

$y = - 2$

$y = - 2$

Step 7

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$3 x + 4 (- 2) = 1$

Multiply $4$ by $- 2$ .

$3 x - 8 = 1$

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

Add $8$ to both sides of the equation.

$3 x = 1 + 8$

Add $1$ and $8$ .

$3 x = 9$

$3 x = 9$

Divide each term in $3 x = 9$ by $3$ and simplify.

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Divide $x$ by $1$ .

$x = \frac{9}{3}$

$x = \frac{9}{3}$

$x = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x = 3$

$x = 3$

$x = 3$

$x = 3$

Step 8

The solution to the independent system of equations can be represented as a point.

$(3, - 2)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(3, - 2)$

Equation Form:

$x = 3, y = - 2$

Step 10

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