Solve the System of Equations x+y=3 2x+2y=6

$x + y = 3$ $2 x + 2 y = 6$

Subtract $y$ from both sides of the equation.

$x = 3 - y$

$2 x + 2 y = 6$

Replace all occurrences of $x$ with $3 - y$ in each equation.

Replace all occurrences of $x$ in $2 x + 2 y = 6$ with $3 - y$ .

$2 (3 - y) + 2 y = 6$

$x = 3 - y$

Simplify the left side.

Simplify $2 (3 - y) + 2 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 3 + 2 (- y) + 2 y = 6$

$x = 3 - y$

Multiply $2$ by $3$ .

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

$x = 3 - y$

Multiply $- 1$ by $2$ .

$6 - 2 y + 2 y = 6$

$x = 3 - y$

$6 - 2 y + 2 y = 6$

$x = 3 - y$

Combine the opposite terms in $6 - 2 y + 2 y$ .

Add $- 2 y$ and $2 y$ .

$6 + 0 = 6$

$x = 3 - y$

Add $6$ and $0$ .

$6 = 6$

$x = 3 - y$

$6 = 6$

$x = 3 - y$

$6 = 6$

$x = 3 - y$

$6 = 6$

$x = 3 - y$

$6 = 6$

$x = 3 - y$

Remove any equations from the system that are always true.

$x = 3 - y$

Related Questions