Solve by Substitution 2x+5y=12 , x-6y=-11

$2 x + 5 y = 12$ , $x - 6 y = - 11$

Step 1

Add $6 y$ to both sides of the equation.

$x = - 11 + 6 y$

$2 x + 5 y = 12$

Step 2

Replace all occurrences of $x$ with $- 11 + 6 y$ in each equation.

Replace all occurrences of $x$ in $2 x + 5 y = 12$ with $- 11 + 6 y$ .

$2 (- 11 + 6 y) + 5 y = 12$

$x = - 11 + 6 y$

Simplify the left side.

Simplify $2 (- 11 + 6 y) + 5 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 11 + 2 (6 y) + 5 y = 12$

$x = - 11 + 6 y$

Multiply $2$ by $- 11$ .

$- 22 + 2 (6 y) + 5 y = 12$

$x = - 11 + 6 y$

Multiply $6$ by $2$ .

$- 22 + 12 y + 5 y = 12$

$x = - 11 + 6 y$

$- 22 + 12 y + 5 y = 12$

$x = - 11 + 6 y$

Add $12 y$ and $5 y$ .

$- 22 + 17 y = 12$

$x = - 11 + 6 y$

$- 22 + 17 y = 12$

$x = - 11 + 6 y$

$- 22 + 17 y = 12$

$x = - 11 + 6 y$

$- 22 + 17 y = 12$

$x = - 11 + 6 y$

Step 3

Solve for $y$ in $- 22 + 17 y = 12$ .

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

Add $22$ to both sides of the equation.

$17 y = 12 + 22$

$x = - 11 + 6 y$

Add $12$ and $22$ .

$17 y = 34$

$x = - 11 + 6 y$

$17 y = 34$

$x = - 11 + 6 y$

Divide each term in $17 y = 34$ by $17$ and simplify.

Divide each term in $17 y = 34$ by $17$ .

$\frac{17 y}{17} = \frac{34}{17}$

$x = - 11 + 6 y$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 y}{17} = \frac{34}{17}$

$x = - 11 + 6 y$

Divide $y$ by $1$ .

$y = \frac{34}{17}$

$x = - 11 + 6 y$

$y = \frac{34}{17}$

$x = - 11 + 6 y$

$y = \frac{34}{17}$

$x = - 11 + 6 y$

Simplify the right side.

Divide $34$ by $17$ .

$y = 2$

$x = - 11 + 6 y$

$y = 2$

$x = - 11 + 6 y$

$y = 2$

$x = - 11 + 6 y$

$y = 2$

$x = - 11 + 6 y$

Step 4

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $x = - 11 + 6 y$ with $2$ .

$x = - 11 + 6 (2)$

$y = 2$

Simplify the right side.

Simplify $- 11 + 6 (2)$ .

Multiply $6$ by $2$ .

$x = - 11 + 12$

$y = 2$

Add $- 11$ and $12$ .

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

Step 5

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

$(1, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 2)$

Equation Form:

$x = 1, y = 2$

Step 7

Solve by Substitution 2x+5y=12 , x-6y=-11

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