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

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

Step 1

Subtract $2 x$ from both sides of the equation.

$y = 4 - 2 x$

$x - y = 2$

Step 2

Replace all occurrences of $y$ with $4 - 2 x$ in each equation.

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

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

$y = 4 - 2 x$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = 4 - 2 x$

Multiply $- 1$ by $4$ .

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

$y = 4 - 2 x$

Multiply $- 2$ by $- 1$ .

$x - 4 + 2 x = 2$

$y = 4 - 2 x$

$x - 4 + 2 x = 2$

$y = 4 - 2 x$

Add $x$ and $2 x$ .

$3 x - 4 = 2$

$y = 4 - 2 x$

$3 x - 4 = 2$

$y = 4 - 2 x$

$3 x - 4 = 2$

$y = 4 - 2 x$

$3 x - 4 = 2$

$y = 4 - 2 x$

Step 3

Solve for $x$ in $3 x - 4 = 2$ .

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

Add $4$ to both sides of the equation.

$3 x = 2 + 4$

$y = 4 - 2 x$

Add $2$ and $4$ .

$3 x = 6$

$y = 4 - 2 x$

$3 x = 6$

$y = 4 - 2 x$

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

Divide each term in $3 x = 6$ by $3$ .

$\frac{3 x}{3} = \frac{6}{3}$

$y = 4 - 2 x$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

$y = 4 - 2 x$

Divide $x$ by $1$ .

$x = \frac{6}{3}$

$y = 4 - 2 x$

$x = \frac{6}{3}$

$y = 4 - 2 x$

$x = \frac{6}{3}$

$y = 4 - 2 x$

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

$y = 4 - 2 x$

$x = 2$

$y = 4 - 2 x$

$x = 2$

$y = 4 - 2 x$

$x = 2$

$y = 4 - 2 x$

Step 4

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

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

$y = 4 - 2 \cdot 2$

$x = 2$

Simplify the right side.

Simplify $4 - 2 \cdot 2$ .

Multiply $- 2$ by $2$ .

$y = 4 - 4$

$x = 2$

Subtract $4$ from $4$ .

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

$y = 0$

$x = 2$

Step 5

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

$(2, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 0)$

Equation Form:

$x = 2, y = 0$

Step 7

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

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