Solve the System of Equations 4x+2y=116 x+y=35

$4 x + 2 y = 116$ $x + y = 35$

Subtract $y$ from both sides of the equation.

$x = 35 - y$

$4 x + 2 y = 116$

Replace all occurrences of $x$ with $35 - y$ in each equation.

Replace all occurrences of $x$ in $4 x + 2 y = 116$ with $35 - y$ .

$4 (35 - y) + 2 y = 116$

$x = 35 - y$

Simplify the left side.

Simplify $4 (35 - y) + 2 y$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 35 + 4 (- y) + 2 y = 116$

$x = 35 - y$

Multiply $4$ by $35$ .

$140 + 4 (- y) + 2 y = 116$

$x = 35 - y$

Multiply $- 1$ by $4$ .

$140 - 4 y + 2 y = 116$

$x = 35 - y$

$140 - 4 y + 2 y = 116$

$x = 35 - y$

Add $- 4 y$ and $2 y$ .

$140 - 2 y = 116$

$x = 35 - y$

$140 - 2 y = 116$

$x = 35 - y$

$140 - 2 y = 116$

$x = 35 - y$

$140 - 2 y = 116$

$x = 35 - y$

Solve for $y$ in $140 - 2 y = 116$ .

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

Subtract $140$ from both sides of the equation.

$- 2 y = 116 - 140$

$x = 35 - y$

Subtract $140$ from $116$ .

$- 2 y = - 24$

$x = 35 - y$

$- 2 y = - 24$

$x = 35 - y$

Divide each term in $- 2 y = - 24$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 24$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 24}{- 2}$

$x = 35 - y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 24}{- 2}$

$x = 35 - y$

Divide $y$ by $1$ .

$y = \frac{- 24}{- 2}$

$x = 35 - y$

$y = \frac{- 24}{- 2}$

$x = 35 - y$

$y = \frac{- 24}{- 2}$

$x = 35 - y$

Simplify the right side.

Divide $- 24$ by $- 2$ .

$y = 12$

$x = 35 - y$

$y = 12$

$x = 35 - y$

$y = 12$

$x = 35 - y$

$y = 12$

$x = 35 - y$

Replace all occurrences of $y$ with $12$ in each equation.

Replace all occurrences of $y$ in $x = 35 - y$ with $12$ .

$x = 35 - (12)$

$y = 12$

Simplify the right side.

Simplify $35 - (12)$ .

Multiply $- 1$ by $12$ .

$x = 35 - 12$

$y = 12$

Subtract $12$ from $35$ .

$x = 23$

$y = 12$

$x = 23$

$y = 12$

$x = 23$

$y = 12$

$x = 23$

$y = 12$

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

$(23, 12)$

The result can be shown in multiple forms.

Point Form:

$(23, 12)$

Equation Form:

$x = 23, y = 12$

Solve the System of Equations 4x+2y=116 x+y=35

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