Solve the System of Equations 2x-y=4 y-x=4

$2 x - y = 4$ $y - x = 4$

Step 1

Add $x$ to both sides of the equation.

$y = 4 + x$

$2 x - y = 4$

Step 2

Replace all occurrences of $y$ with $4 + x$ in each equation.

Replace all occurrences of $y$ in $2 x - y = 4$ with $4 + x$ .

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

$y = 4 + x$

Simplify the left side.

Simplify $2 x - (4 + x)$ .

Simplify each term.

Apply the distributive property.

$2 x - 1 \cdot 4 - x = 4$

$y = 4 + x$

Multiply $- 1$ by $4$ .

$2 x - 4 - x = 4$

$y = 4 + x$

$2 x - 4 - x = 4$

$y = 4 + x$

Subtract $x$ from $2 x$ .

$x - 4 = 4$

$y = 4 + x$

$x - 4 = 4$

$y = 4 + x$

$x - 4 = 4$

$y = 4 + x$

$x - 4 = 4$

$y = 4 + x$

Step 3

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

Add $4$ to both sides of the equation.

$x = 4 + 4$

$y = 4 + x$

Add $4$ and $4$ .

$x = 8$

$y = 4 + x$

$x = 8$

$y = 4 + x$

Step 4

Replace all occurrences of $x$ with $8$ in each equation.

Replace all occurrences of $x$ in $y = 4 + x$ with $8$ .

$y = 4 + 8$

$x = 8$

Simplify $y = 4 + 8$ .

Simplify the left side.

Remove parentheses.

$y = 4 + 8$

$x = 8$

$y = 4 + 8$

$x = 8$

Simplify the right side.

Add $4$ and $8$ .

$y = 12$

$x = 8$

$y = 12$

$x = 8$

$y = 12$

$x = 8$

$y = 12$

$x = 8$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(8, 12)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8, 12)$

Equation Form:

$x = 8, y = 12$

Step 7

Solve the System of Equations 2x-y=4 y-x=4

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