Solve the System of @WORD x+y=6 , y=3x

$x + y = 6$ , $y = 3 x$

Step 1

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

Replace all occurrences of $y$ in $x + y = 6$ with $3 x$ .

$x + 3 x = 6$

$y = 3 x$

Simplify the left side.

Simplify $x + 3 x$ .

Remove parentheses.

$x + 3 x = 6$

$y = 3 x$

Add $x$ and $3 x$ .

$4 x = 6$

$y = 3 x$

$4 x = 6$

$y = 3 x$

$4 x = 6$

$y = 3 x$

$4 x = 6$

$y = 3 x$

Step 2

Divide each term in $4 x = 6$ by $4$ and simplify.

Divide each term in $4 x = 6$ by $4$ .

$\frac{4 x}{4} = \frac{6}{4}$

$y = 3 x$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{6}{4}$

$y = 3 x$

Divide $x$ by $1$ .

$x = \frac{6}{4}$

$y = 3 x$

$x = \frac{6}{4}$

$y = 3 x$

$x = \frac{6}{4}$

$y = 3 x$

Simplify the right side.

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{4}$

$y = 3 x$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 3}{2 \cdot 2}$

$y = 3 x$

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 2}$

$y = 3 x$

Rewrite the expression.

$x = \frac{3}{2}$

$y = 3 x$

$x = \frac{3}{2}$

$y = 3 x$

$x = \frac{3}{2}$

$y = 3 x$

$x = \frac{3}{2}$

$y = 3 x$

$x = \frac{3}{2}$

$y = 3 x$

Step 3

Replace all occurrences of $x$ with $\frac{3}{2}$ in each equation.

Replace all occurrences of $x$ in $y = 3 x$ with $\frac{3}{2}$ .

$y = 3 (\frac{3}{2})$

$x = \frac{3}{2}$

Simplify the right side.

Multiply $3 (\frac{3}{2})$ .

Combine $3$ and $\frac{3}{2}$ .

$y = \frac{3 \cdot 3}{2}$

$x = \frac{3}{2}$

Multiply $3$ by $3$ .

$y = \frac{9}{2}$

$x = \frac{3}{2}$

$y = \frac{9}{2}$

$x = \frac{3}{2}$

$y = \frac{9}{2}$

$x = \frac{3}{2}$

$y = \frac{9}{2}$

$x = \frac{3}{2}$

Step 4

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

$(\frac{3}{2}, \frac{9}{2})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{3}{2}, \frac{9}{2})$

Equation Form:

$x = \frac{3}{2}, y = \frac{9}{2}$

Step 6

Solve the System of @WORD x+y=6 , y=3x

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