Solve by Substitution 2x+y=4 , y=2x

$2 x + y = 4$ , $y = 2 x$

Step 1

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

Replace all occurrences of $y$ in $2 x + y = 4$ with $2 x$ .

$2 x + 2 x = 4$

$y = 2 x$

Simplify the left side.

Simplify $2 x + 2 x$ .

Remove parentheses.

$2 x + 2 x = 4$

$y = 2 x$

Add $2 x$ and $2 x$ .

$4 x = 4$

$y = 2 x$

$4 x = 4$

$y = 2 x$

$4 x = 4$

$y = 2 x$

$4 x = 4$

$y = 2 x$

Step 2

Divide each term in $4 x = 4$ by $4$ and simplify.

Divide each term in $4 x = 4$ by $4$ .

$\frac{4 x}{4} = \frac{4}{4}$

$y = 2 x$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{4}{4}$

$y = 2 x$

Divide $x$ by $1$ .

$x = \frac{4}{4}$

$y = 2 x$

$x = \frac{4}{4}$

$y = 2 x$

$x = \frac{4}{4}$

$y = 2 x$

Simplify the right side.

Divide $4$ by $4$ .

$x = 1$

$y = 2 x$

$x = 1$

$y = 2 x$

$x = 1$

$y = 2 x$

Step 3

Replace all occurrences of $x$ with $1$ in each equation.

Replace all occurrences of $x$ in $y = 2 x$ with $1$ .

$y = 2 (1)$

$x = 1$

Simplify the right side.

Multiply $2$ by $1$ .

$y = 2$

$x = 1$

$y = 2$

$x = 1$

$y = 2$

$x = 1$

Step 4

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

$(1, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 2)$

Equation Form:

$x = 1, y = 2$

Step 6

Solve by Substitution 2x+y=4 , y=2x

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