Solve by Substitution x+y=9 , y=2x

$x + y = 9$ , $y = 2 x$

Step 1

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

Replace all occurrences of $y$ in $x + y = 9$ with $2 x$ .

$x + 2 x = 9$

$y = 2 x$

Simplify the left side.

Simplify $x + 2 x$ .

Remove parentheses.

$x + 2 x = 9$

$y = 2 x$

Add $x$ and $2 x$ .

$3 x = 9$

$y = 2 x$

$3 x = 9$

$y = 2 x$

$3 x = 9$

$y = 2 x$

$3 x = 9$

$y = 2 x$

Step 2

Divide each term in $3 x = 9$ by $3$ and simplify.

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

$y = 2 x$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

$y = 2 x$

Divide $x$ by $1$ .

$x = \frac{9}{3}$

$y = 2 x$

$x = \frac{9}{3}$

$y = 2 x$

$x = \frac{9}{3}$

$y = 2 x$

Simplify the right side.

Divide $9$ by $3$ .

$x = 3$

$y = 2 x$

$x = 3$

$y = 2 x$

$x = 3$

$y = 2 x$

Step 3

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

Replace all occurrences of $x$ in $y = 2 x$ with $3$ .

$y = 2 (3)$

$x = 3$

Simplify the right side.

Multiply $2$ by $3$ .

$y = 6$

$x = 3$

$y = 6$

$x = 3$

$y = 6$

$x = 3$

Step 4

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

$(3, 6)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(3, 6)$

Equation Form:

$x = 3, y = 6$

Step 6

Solve by Substitution x+y=9 , y=2x

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