Solve by Substitution 2x+6y=24 , 5x-2y=9

$2 x + 6 y = 24$ , $5 x - 2 y = 9$

Step 1

Solve for $x$ in $2 x + 6 y = 24$ .

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

$2 x = 24 - 6 y$

$5 x - 2 y = 9$

Divide each term in $2 x = 24 - 6 y$ by $2$ and simplify.

Divide each term in $2 x = 24 - 6 y$ by $2$ .

$\frac{2 x}{2} = \frac{24}{2} + \frac{- 6 y}{2}$

$5 x - 2 y = 9$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{24}{2} + \frac{- 6 y}{2}$

$5 x - 2 y = 9$

Divide $x$ by $1$ .

$x = \frac{24}{2} + \frac{- 6 y}{2}$

$5 x - 2 y = 9$

$x = \frac{24}{2} + \frac{- 6 y}{2}$

$5 x - 2 y = 9$

$x = \frac{24}{2} + \frac{- 6 y}{2}$

$5 x - 2 y = 9$

Simplify the right side.

Simplify each term.

Divide $24$ by $2$ .

$x = 12 + \frac{- 6 y}{2}$

$5 x - 2 y = 9$

Cancel the common factor of $- 6$ and $2$ .

Factor $2$ out of $- 6 y$ .

$x = 12 + \frac{2 (- 3 y)}{2}$

$5 x - 2 y = 9$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = 12 + \frac{2 (- 3 y)}{2 (1)}$

$5 x - 2 y = 9$

Cancel the common factor.

$x = 12 + \frac{2 (- 3 y)}{2 \cdot 1}$

$5 x - 2 y = 9$

Rewrite the expression.

$x = 12 + \frac{- 3 y}{1}$

$5 x - 2 y = 9$

Divide $- 3 y$ by $1$ .

$x = 12 - 3 y$

$5 x - 2 y = 9$

$x = 12 - 3 y$

$5 x - 2 y = 9$

$x = 12 - 3 y$

$5 x - 2 y = 9$

$x = 12 - 3 y$

$5 x - 2 y = 9$

$x = 12 - 3 y$

$5 x - 2 y = 9$

$x = 12 - 3 y$

$5 x - 2 y = 9$

$x = 12 - 3 y$

$5 x - 2 y = 9$

Step 2

Replace all occurrences of $x$ with $12 - 3 y$ in each equation.

Replace all occurrences of $x$ in $5 x - 2 y = 9$ with $12 - 3 y$ .

$5 (12 - 3 y) - 2 y = 9$

$x = 12 - 3 y$

Simplify the left side.

Simplify $5 (12 - 3 y) - 2 y$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 12 + 5 (- 3 y) - 2 y = 9$

$x = 12 - 3 y$

Multiply $5$ by $12$ .

$60 + 5 (- 3 y) - 2 y = 9$

$x = 12 - 3 y$

Multiply $- 3$ by $5$ .

$60 - 15 y - 2 y = 9$

$x = 12 - 3 y$

$60 - 15 y - 2 y = 9$

$x = 12 - 3 y$

Subtract $2 y$ from $- 15 y$ .

$60 - 17 y = 9$

$x = 12 - 3 y$

$60 - 17 y = 9$

$x = 12 - 3 y$

$60 - 17 y = 9$

$x = 12 - 3 y$

$60 - 17 y = 9$

$x = 12 - 3 y$

Step 3

Solve for $y$ in $60 - 17 y = 9$ .

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

Subtract $60$ from both sides of the equation.

$- 17 y = 9 - 60$

$x = 12 - 3 y$

Subtract $60$ from $9$ .

$- 17 y = - 51$

$x = 12 - 3 y$

$- 17 y = - 51$

$x = 12 - 3 y$

Divide each term in $- 17 y = - 51$ by $- 17$ and simplify.

Divide each term in $- 17 y = - 51$ by $- 17$ .

$\frac{- 17 y}{- 17} = \frac{- 51}{- 17}$

$x = 12 - 3 y$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 y}{- 17} = \frac{- 51}{- 17}$

$x = 12 - 3 y$

Divide $y$ by $1$ .

$y = \frac{- 51}{- 17}$

$x = 12 - 3 y$

$y = \frac{- 51}{- 17}$

$x = 12 - 3 y$

$y = \frac{- 51}{- 17}$

$x = 12 - 3 y$

Simplify the right side.

Divide $- 51$ by $- 17$ .

$y = 3$

$x = 12 - 3 y$

$y = 3$

$x = 12 - 3 y$

$y = 3$

$x = 12 - 3 y$

$y = 3$

$x = 12 - 3 y$

Step 4

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

Replace all occurrences of $y$ in $x = 12 - 3 y$ with $3$ .

$x = 12 - 3 \cdot 3$

$y = 3$

Simplify the right side.

Simplify $12 - 3 \cdot 3$ .

Multiply $- 3$ by $3$ .

$x = 12 - 9$

$y = 3$

Subtract $9$ from $12$ .

$x = 3$

$y = 3$

$x = 3$

$y = 3$

$x = 3$

$y = 3$

$x = 3$

$y = 3$

Step 5

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

$(3, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 3)$

Equation Form:

$x = 3, y = 3$

Step 7

Solve by Substitution 2x+6y=24 , 5x-2y=9

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