Solve by Substitution x+y=12 y=5x

$x + y = 12$ $y = 5 x$

Step 1

Replace all occurrences of $y$ with $5 x$ in each equation.

Replace all occurrences of $y$ in $x + y = 12$ with $5 x$ .

$x + 5 x = 12$

$y = 5 x$

Simplify the left side.

Simplify $x + 5 x$ .

Remove parentheses.

$x + 5 x = 12$

$y = 5 x$

Add $x$ and $5 x$ .

$6 x = 12$

$y = 5 x$

$6 x = 12$

$y = 5 x$

$6 x = 12$

$y = 5 x$

$6 x = 12$

$y = 5 x$

Step 2

Divide each term in $6 x = 12$ by $6$ and simplify.

Divide each term in $6 x = 12$ by $6$ .

$\frac{6 x}{6} = \frac{12}{6}$

$y = 5 x$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{12}{6}$

$y = 5 x$

Divide $x$ by $1$ .

$x = \frac{12}{6}$

$y = 5 x$

$x = \frac{12}{6}$

$y = 5 x$

$x = \frac{12}{6}$

$y = 5 x$

Simplify the right side.

Divide $12$ by $6$ .

$x = 2$

$y = 5 x$

$x = 2$

$y = 5 x$

$x = 2$

$y = 5 x$

Step 3

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

Replace all occurrences of $x$ in $y = 5 x$ with $2$ .

$y = 5 (2)$

$x = 2$

Simplify the right side.

Multiply $5$ by $2$ .

$y = 10$

$x = 2$

$y = 10$

$x = 2$

$y = 10$

$x = 2$

Step 4

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

$(2, 10)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 10)$

Equation Form:

$x = 2, y = 10$

Step 6

Solve by Substitution x+y=12 y=5x

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