Solve the System of Equations y=3x 2y+x=14

$y = 3 x$ $2 y + x = 14$

Step 1

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

Replace all occurrences of $y$ in $2 y + x = 14$ with $3 x$ .

$2 (3 x) + x = 14$

$y = 3 x$

Simplify the left side.

Simplify $2 (3 x) + x$ .

Multiply $3$ by $2$ .

$6 x + x = 14$

$y = 3 x$

Add $6 x$ and $x$ .

$7 x = 14$

$y = 3 x$

$7 x = 14$

$y = 3 x$

$7 x = 14$

$y = 3 x$

$7 x = 14$

$y = 3 x$

Step 2

Divide each term in $7 x = 14$ by $7$ and simplify.

Divide each term in $7 x = 14$ by $7$ .

$\frac{7 x}{7} = \frac{14}{7}$

$y = 3 x$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{14}{7}$

$y = 3 x$

Divide $x$ by $1$ .

$x = \frac{14}{7}$

$y = 3 x$

$x = \frac{14}{7}$

$y = 3 x$

$x = \frac{14}{7}$

$y = 3 x$

Simplify the right side.

Divide $14$ by $7$ .

$x = 2$

$y = 3 x$

$x = 2$

$y = 3 x$

$x = 2$

$y = 3 x$

Step 3

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

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

$y = 3 (2)$

$x = 2$

Simplify the right side.

Multiply $3$ by $2$ .

$y = 6$

$x = 2$

$y = 6$

$x = 2$

$y = 6$

$x = 2$

Step 4

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

$(2, 6)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 6)$

Equation Form:

$x = 2, y = 6$

Step 6

Solve the System of Equations y=3x 2y+x=14

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