Solve by Addition/Elimination y-x=2 y=-1/4x+7

$y - x = 2$ $y = - \frac{1}{4} x + 7$

Multiply each term in $y = - \frac{1}{4} x + 7$ by $4$ to eliminate the fractions.

Multiply each term in $y = - \frac{1}{4} x + 7$ by $4$ .

$y \cdot 4 = - \frac{1}{4} x \cdot 4 + 7 \cdot 4$

$y - x = 2$

Simplify the left side.

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

$4 y = - \frac{1}{4} x \cdot 4 + 7 \cdot 4$

$y - x = 2$

$4 y = - \frac{1}{4} x \cdot 4 + 7 \cdot 4$

$y - x = 2$

Simplify the right side.

Simplify each term.

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

$4 y = - \frac{x}{4} \cdot 4 + 7 \cdot 4$

$y - x = 2$

Cancel the common factor of $4$ .

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

$4 y = \frac{- x}{4} \cdot 4 + 7 \cdot 4$

$y - x = 2$

Cancel the common factor.

$4 y = \frac{- x}{4} \cdot 4 + 7 \cdot 4$

$y - x = 2$

Rewrite the expression.

$4 y = - x + 7 \cdot 4$

$y - x = 2$

$4 y = - x + 7 \cdot 4$

$y - x = 2$

Multiply $7$ by $4$ .

$4 y = - x + 28$

$y - x = 2$

$4 y = - x + 28$

$y - x = 2$

$4 y = - x + 28$

$y - x = 2$

$4 y = - x + 28$

$y - x = 2$

Simplify the left side.

Reorder $y$ and $- x$ .

$- x + y = 2$

$4 y = - x + 28$

$- x + y = 2$

$4 y = - x + 28$

Move all terms containing variables to the left side of the equation.

Add $x$ to both sides of the equation.

$4 y + x = 28$

$- x + y = 2$

Reorder $4 y$ and $x$ .

$x + 4 y = 28$

$- x + y = 2$

$x + 4 y = 28$

$- x + y = 2$

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

	$-$	$x$	$+$		$y$	$=$		$2$
$+$		$x$	$+$	$4$	$y$	$=$	$2$	$8$
				$5$	$y$	$=$	$3$	$0$

Divide each term in $5 y = 30$ by $5$ and simplify.

Divide each term in $5 y = 30$ by $5$ .

$\frac{5 y}{5} = \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{30}{5}$

Divide $y$ by $1$ .

$y = \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$y = 6$

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 $x$ .

$- x + 6 = 2$

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

Subtract $6$ from both sides of the equation.

$- x = 2 - 6$

Subtract $6$ from $2$ .

$- x = - 4$

Divide each term in $- x = - 4$ by $- 1$ and simplify.

Divide each term in $- x = - 4$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $- 1$ .

$x = 4$

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

$(4, 6)$

The result can be shown in multiple forms.

Point Form:

$(4, 6)$

Equation Form:

$x = 4, y = 6$

Solve by Addition/Elimination y-x=2 y=-1/4x+7

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