Solve by Substitution x+y=6 2x+y=4

$x + y = 6$ $2 x + y = 4$

Step 1

Subtract $y$ from both sides of the equation.

$x = 6 - y$

$2 x + y = 4$

Step 2

Replace all occurrences of $x$ with $6 - y$ in each equation.

Replace all occurrences of $x$ in $2 x + y = 4$ with $6 - y$ .

$2 (6 - y) + y = 4$

$x = 6 - y$

Simplify the left side.

Simplify $2 (6 - y) + y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 6 + 2 (- y) + y = 4$

$x = 6 - y$

Multiply $2$ by $6$ .

$12 + 2 (- y) + y = 4$

$x = 6 - y$

Multiply $- 1$ by $2$ .

$12 - 2 y + y = 4$

$x = 6 - y$

$12 - 2 y + y = 4$

$x = 6 - y$

Add $- 2 y$ and $y$ .

$12 - y = 4$

$x = 6 - y$

$12 - y = 4$

$x = 6 - y$

$12 - y = 4$

$x = 6 - y$

$12 - y = 4$

$x = 6 - y$

Step 3

Solve for $y$ in $12 - y = 4$ .

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

Subtract $12$ from both sides of the equation.

$- y = 4 - 12$

$x = 6 - y$

Subtract $12$ from $4$ .

$- y = - 8$

$x = 6 - y$

$- y = - 8$

$x = 6 - y$

Divide each term in $- y = - 8$ by $- 1$ and simplify.

Divide each term in $- y = - 8$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 8}{- 1}$

$x = 6 - y$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 8}{- 1}$

$x = 6 - y$

Divide $y$ by $1$ .

$y = \frac{- 8}{- 1}$

$x = 6 - y$

$y = \frac{- 8}{- 1}$

$x = 6 - y$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$y = 8$

$x = 6 - y$

$y = 8$

$x = 6 - y$

$y = 8$

$x = 6 - y$

$y = 8$

$x = 6 - y$

Step 4

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

Replace all occurrences of $y$ in $x = 6 - y$ with $8$ .

$x = 6 - (8)$

$y = 8$

Simplify the right side.

Simplify $6 - (8)$ .

Multiply $- 1$ by $8$ .

$x = 6 - 8$

$y = 8$

Subtract $8$ from $6$ .

$x = - 2$

$y = 8$

$x = - 2$

$y = 8$

$x = - 2$

$y = 8$

$x = - 2$

$y = 8$

Step 5

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

$(- 2, 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, 8)$

Equation Form:

$x = - 2, y = 8$

Step 7

Solve by Substitution x+y=6 2x+y=4

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