Solve the System of Equations 2y+x=-15 x=3y

$2 y + x = - 15$ $x = 3 y$

Step 1

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

Replace all occurrences of $x$ in $2 y + x = - 15$ with $3 y$ .

$2 y + 3 y = - 15$

$x = 3 y$

Simplify the left side.

Simplify $2 y + 3 y$ .

Remove parentheses.

$2 y + 3 y = - 15$

$x = 3 y$

Add $2 y$ and $3 y$ .

$5 y = - 15$

$x = 3 y$

$5 y = - 15$

$x = 3 y$

$5 y = - 15$

$x = 3 y$

$5 y = - 15$

$x = 3 y$

Step 2

Divide each term in $5 y = - 15$ by $5$ and simplify.

Divide each term in $5 y = - 15$ by $5$ .

$\frac{5 y}{5} = \frac{- 15}{5}$

$x = 3 y$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 15}{5}$

$x = 3 y$

Divide $y$ by $1$ .

$y = \frac{- 15}{5}$

$x = 3 y$

$y = \frac{- 15}{5}$

$x = 3 y$

$y = \frac{- 15}{5}$

$x = 3 y$

Simplify the right side.

Divide $- 15$ by $5$ .

$y = - 3$

$x = 3 y$

$y = - 3$

$x = 3 y$

$y = - 3$

$x = 3 y$

Step 3

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

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

$x = 3 (- 3)$

$y = - 3$

Simplify the right side.

Multiply $3$ by $- 3$ .

$x = - 9$

$y = - 3$

$x = - 9$

$y = - 3$

$x = - 9$

$y = - 3$

Step 4

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

$(- 9, - 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 9, - 3)$

Equation Form:

$x = - 9, y = - 3$

Step 6

Solve the System of Equations 2y+x=-15 x=3y

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