Solve the System of Equations y-x=2 y=-1/4x+7

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

Step 1

Add $x$ to both sides of the equation.

$y = 2 + x$

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

Step 2

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

Replace all occurrences of $y$ in $y = 2 + x$ with $2 + x$ .

$2 + x = 2 + x$

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

Simplify the left side.

Remove parentheses.

$2 + x = 2 + x$

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

$2 + x = 2 + x$

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

Replace all occurrences of $y$ in $y = - \frac{1}{4} x + 7$ with $2 + x$ .

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

$2 + x = 2 + x$

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

Simplify the left side.

Remove parentheses.

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

$2 + x = 2 + x$

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

$2 + x = 2 + x$

Simplify the right side.

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

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

$2 + x = 2 + x$

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

$2 + x = 2 + x$

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

$2 + x = 2 + x$

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

$2 + x = 2 + x$

Step 3

Remove any equations from the system that are always true.

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

Step 4

Solve for $x$ in $2 + x = - \frac{x}{4} + 7$ .

Move all terms containing $x$ to the left side of the equation.

Add $\frac{x}{4}$ to both sides of the equation.

$2 + x + \frac{x}{4} = 7$

To write $x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$2 + x \cdot \frac{4}{4} + \frac{x}{4} = 7$

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

$2 + \frac{x \cdot 4}{4} + \frac{x}{4} = 7$

Combine the numerators over the common denominator.

$2 + \frac{x \cdot 4 + x}{4} = 7$

Add $x \cdot 4$ and $x$ .

Reorder $x$ and $4$ .

$2 + \frac{4 \cdot x + x}{4} = 7$

Add $4 \cdot x$ and $x$ .

$2 + \frac{5 \cdot x}{4} = 7$

$2 + \frac{5 x}{4} = 7$

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

Subtract $2$ from both sides of the equation.

$\frac{5 x}{4} = 7 - 2$

Subtract $2$ from $7$ .

$\frac{5 x}{4} = 5$

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot 5$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{5} \cdot \frac{5 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot 5$

Rewrite the expression.

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

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{4}{5} \cdot 5$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

$x = \frac{4}{5} \cdot 5$

Rewrite the expression.

$x = 4$

Step 5

Solve the System of Equations y-x=2 y=-1/4x+7

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