Solve the System of Equations 9x+5y=41 and x+y=9

$9 x + 5 y = 41$ and $x + y = 9$

Subtract $y$ from both sides of the equation.

$x = 9 - y$

$9 x + 5 y = 41$

Replace all occurrences of $x$ with $9 - y$ in each equation.

Replace all occurrences of $x$ in $9 x + 5 y = 41$ with $9 - y$ .

$9 (9 - y) + 5 y = 41$

$x = 9 - y$

Simplify the left side.

Simplify $9 (9 - y) + 5 y$ .

Simplify each term.

Apply the distributive property.

$9 \cdot 9 + 9 (- y) + 5 y = 41$

$x = 9 - y$

Multiply $9$ by $9$ .

$81 + 9 (- y) + 5 y = 41$

$x = 9 - y$

Multiply $- 1$ by $9$ .

$81 - 9 y + 5 y = 41$

$x = 9 - y$

$81 - 9 y + 5 y = 41$

$x = 9 - y$

Add $- 9 y$ and $5 y$ .

$81 - 4 y = 41$

$x = 9 - y$

$81 - 4 y = 41$

$x = 9 - y$

$81 - 4 y = 41$

$x = 9 - y$

$81 - 4 y = 41$

$x = 9 - y$

Solve for $y$ in $81 - 4 y = 41$ .

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

Subtract $81$ from both sides of the equation.

$- 4 y = 41 - 81$

$x = 9 - y$

Subtract $81$ from $41$ .

$- 4 y = - 40$

$x = 9 - y$

$- 4 y = - 40$

$x = 9 - y$

Divide each term in $- 4 y = - 40$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 40$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 40}{- 4}$

$x = 9 - y$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 40}{- 4}$

$x = 9 - y$

Divide $y$ by $1$ .

$y = \frac{- 40}{- 4}$

$x = 9 - y$

$y = \frac{- 40}{- 4}$

$x = 9 - y$

$y = \frac{- 40}{- 4}$

$x = 9 - y$

Simplify the right side.

Divide $- 40$ by $- 4$ .

$y = 10$

$x = 9 - y$

$y = 10$

$x = 9 - y$

$y = 10$

$x = 9 - y$

$y = 10$

$x = 9 - y$

Replace all occurrences of $y$ with $10$ in each equation.

Replace all occurrences of $y$ in $x = 9 - y$ with $10$ .

$x = 9 - (10)$

$y = 10$

Simplify the right side.

Simplify $9 - (10)$ .

Multiply $- 1$ by $10$ .

$x = 9 - 10$

$y = 10$

Subtract $10$ from $9$ .

$x = - 1$

$y = 10$

$x = - 1$

$y = 10$

$x = - 1$

$y = 10$

$x = - 1$

$y = 10$

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

$(- 1, 10)$

The result can be shown in multiple forms.

Point Form:

$(- 1, 10)$

Equation Form:

$x = - 1, y = 10$

Solve the System of Equations 9x+5y=41 and x+y=9

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