Solve by Substitution x+y=14 , x=6y

$x + y = 14$ , $x = 6 y$

Step 1

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

Replace all occurrences of $x$ in $x + y = 14$ with $6 y$ .

$(6 y) + y = 14$

$x = 6 y$

Simplify the left side.

Add $6 y$ and $y$ .

$7 y = 14$

$x = 6 y$

$7 y = 14$

$x = 6 y$

$7 y = 14$

$x = 6 y$

Step 2

Divide each term in $7 y = 14$ by $7$ and simplify.

Divide each term in $7 y = 14$ by $7$ .

$\frac{7 y}{7} = \frac{14}{7}$

$x = 6 y$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{14}{7}$

$x = 6 y$

Divide $y$ by $1$ .

$y = \frac{14}{7}$

$x = 6 y$

$y = \frac{14}{7}$

$x = 6 y$

$y = \frac{14}{7}$

$x = 6 y$

Simplify the right side.

Divide $14$ by $7$ .

$y = 2$

$x = 6 y$

$y = 2$

$x = 6 y$

$y = 2$

$x = 6 y$

Step 3

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

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

$x = 6 (2)$

$y = 2$

Simplify the right side.

Multiply $6$ by $2$ .

$x = 12$

$y = 2$

$x = 12$

$y = 2$

$x = 12$

$y = 2$

Step 4

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

$(12, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(12, 2)$

Equation Form:

$x = 12, y = 2$

Step 6

Solve by Substitution x+y=14 , x=6y

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