Solve the System of Equations x+6y=27 7x-3y=9

$x + 6 y = 27$ $7 x - 3 y = 9$

Step 1

Subtract $6 y$ from both sides of the equation.

$x = 27 - 6 y$

$7 x - 3 y = 9$

Step 2

Replace all occurrences of $x$ with $27 - 6 y$ in each equation.

Replace all occurrences of $x$ in $7 x - 3 y = 9$ with $27 - 6 y$ .

$7 (27 - 6 y) - 3 y = 9$

$x = 27 - 6 y$

Simplify the left side.

Simplify $7 (27 - 6 y) - 3 y$ .

Simplify each term.

Apply the distributive property.

$7 \cdot 27 + 7 (- 6 y) - 3 y = 9$

$x = 27 - 6 y$

Multiply $7$ by $27$ .

$189 + 7 (- 6 y) - 3 y = 9$

$x = 27 - 6 y$

Multiply $- 6$ by $7$ .

$189 - 42 y - 3 y = 9$

$x = 27 - 6 y$

$189 - 42 y - 3 y = 9$

$x = 27 - 6 y$

Subtract $3 y$ from $- 42 y$ .

$189 - 45 y = 9$

$x = 27 - 6 y$

$189 - 45 y = 9$

$x = 27 - 6 y$

$189 - 45 y = 9$

$x = 27 - 6 y$

$189 - 45 y = 9$

$x = 27 - 6 y$

Step 3

Solve for $y$ in $189 - 45 y = 9$ .

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

Subtract $189$ from both sides of the equation.

$- 45 y = 9 - 189$

$x = 27 - 6 y$

Subtract $189$ from $9$ .

$- 45 y = - 180$

$x = 27 - 6 y$

$- 45 y = - 180$

$x = 27 - 6 y$

Divide each term in $- 45 y = - 180$ by $- 45$ and simplify.

Divide each term in $- 45 y = - 180$ by $- 45$ .

$\frac{- 45 y}{- 45} = \frac{- 180}{- 45}$

$x = 27 - 6 y$

Simplify the left side.

Cancel the common factor of $- 45$ .

Cancel the common factor.

$\frac{- 45 y}{- 45} = \frac{- 180}{- 45}$

$x = 27 - 6 y$

Divide $y$ by $1$ .

$y = \frac{- 180}{- 45}$

$x = 27 - 6 y$

$y = \frac{- 180}{- 45}$

$x = 27 - 6 y$

$y = \frac{- 180}{- 45}$

$x = 27 - 6 y$

Simplify the right side.

Divide $- 180$ by $- 45$ .

$y = 4$

$x = 27 - 6 y$

$y = 4$

$x = 27 - 6 y$

$y = 4$

$x = 27 - 6 y$

$y = 4$

$x = 27 - 6 y$

Step 4

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

Replace all occurrences of $y$ in $x = 27 - 6 y$ with $4$ .

$x = 27 - 6 \cdot 4$

$y = 4$

Simplify the right side.

Simplify $27 - 6 \cdot 4$ .

Multiply $- 6$ by $4$ .

$x = 27 - 24$

$y = 4$

Subtract $24$ from $27$ .

$x = 3$

$y = 4$

$x = 3$

$y = 4$

$x = 3$

$y = 4$

$x = 3$

$y = 4$

Step 5

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

$(3, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 4)$

Equation Form:

$x = 3, y = 4$

Step 7

Solve the System of Equations x+6y=27 7x-3y=9

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