Solve the System of Equations 2x+y=7 x-2y=6

$2 x + y = 7$ $x - 2 y = 6$

Step 1

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

$y = 7 - 2 x$

$x - 2 y = 6$

Step 2

Replace all occurrences of $y$ with $7 - 2 x$ in each equation.

Replace all occurrences of $y$ in $x - 2 y = 6$ with $7 - 2 x$ .

$x - 2 (7 - 2 x) = 6$

$y = 7 - 2 x$

Simplify the left side.

Simplify $x - 2 (7 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$x - 2 \cdot 7 - 2 (- 2 x) = 6$

$y = 7 - 2 x$

Multiply $- 2$ by $7$ .

$x - 14 - 2 (- 2 x) = 6$

$y = 7 - 2 x$

Multiply $- 2$ by $- 2$ .

$x - 14 + 4 x = 6$

$y = 7 - 2 x$

$x - 14 + 4 x = 6$

$y = 7 - 2 x$

Add $x$ and $4 x$ .

$5 x - 14 = 6$

$y = 7 - 2 x$

$5 x - 14 = 6$

$y = 7 - 2 x$

$5 x - 14 = 6$

$y = 7 - 2 x$

$5 x - 14 = 6$

$y = 7 - 2 x$

Step 3

Solve for $x$ in $5 x - 14 = 6$ .

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

Add $14$ to both sides of the equation.

$5 x = 6 + 14$

$y = 7 - 2 x$

Add $6$ and $14$ .

$5 x = 20$

$y = 7 - 2 x$

$5 x = 20$

$y = 7 - 2 x$

Divide each term in $5 x = 20$ by $5$ and simplify.

Divide each term in $5 x = 20$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5}$

$y = 7 - 2 x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5}$

$y = 7 - 2 x$

Divide $x$ by $1$ .

$x = \frac{20}{5}$

$y = 7 - 2 x$

$x = \frac{20}{5}$

$y = 7 - 2 x$

$x = \frac{20}{5}$

$y = 7 - 2 x$

Simplify the right side.

Divide $20$ by $5$ .

$x = 4$

$y = 7 - 2 x$

$x = 4$

$y = 7 - 2 x$

$x = 4$

$y = 7 - 2 x$

$x = 4$

$y = 7 - 2 x$

Step 4

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

Replace all occurrences of $x$ in $y = 7 - 2 x$ with $4$ .

$y = 7 - 2 \cdot 4$

$x = 4$

Simplify the right side.

Simplify $7 - 2 \cdot 4$ .

Multiply $- 2$ by $4$ .

$y = 7 - 8$

$x = 4$

Subtract $8$ from $7$ .

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

Step 5

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

$(4, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, - 1)$

Equation Form:

$x = 4, y = - 1$

Step 7

Solve the System of Equations 2x+y=7 x-2y=6

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