Solve by Substitution x+y=5 , y=4x

$x + y = 5$ , $y = 4 x$

Step 1

Replace all occurrences of $y$ with $4 x$ in each equation.

Replace all occurrences of $y$ in $x + y = 5$ with $4 x$ .

$x + 4 x = 5$

$y = 4 x$

Simplify the left side.

Simplify $x + 4 x$ .

Remove parentheses.

$x + 4 x = 5$

$y = 4 x$

Add $x$ and $4 x$ .

$5 x = 5$

$y = 4 x$

$5 x = 5$

$y = 4 x$

$5 x = 5$

$y = 4 x$

$5 x = 5$

$y = 4 x$

Step 2

Divide each term in $5 x = 5$ by $5$ and simplify.

Divide each term in $5 x = 5$ by $5$ .

$\frac{5 x}{5} = \frac{5}{5}$

$y = 4 x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{5}{5}$

$y = 4 x$

Divide $x$ by $1$ .

$x = \frac{5}{5}$

$y = 4 x$

$x = \frac{5}{5}$

$y = 4 x$

$x = \frac{5}{5}$

$y = 4 x$

Simplify the right side.

Divide $5$ by $5$ .

$x = 1$

$y = 4 x$

$x = 1$

$y = 4 x$

$x = 1$

$y = 4 x$

Step 3

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

Replace all occurrences of $x$ in $y = 4 x$ with $1$ .

$y = 4 (1)$

$x = 1$

Simplify the right side.

Multiply $4$ by $1$ .

$y = 4$

$x = 1$

$y = 4$

$x = 1$

$y = 4$

$x = 1$

Step 4

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

$(1, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 4)$

Equation Form:

$x = 1, y = 4$

Step 6

Solve by Substitution x+y=5 , y=4x

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