Solve the System of Equations y-15=3x -2x+5y=-3

$y - 15 = 3 x$ $- 2 x + 5 y = - 3$

Step 1

Add $15$ to both sides of the equation.

$y = 3 x + 15$

$- 2 x + 5 y = - 3$

Step 2

Replace all occurrences of $y$ with $3 x + 15$ in each equation.

Replace all occurrences of $y$ in $- 2 x + 5 y = - 3$ with $3 x + 15$ .

$- 2 x + 5 (3 x + 15) = - 3$

$y = 3 x + 15$

Simplify the left side.

Simplify $- 2 x + 5 (3 x + 15)$ .

Simplify each term.

Apply the distributive property.

$- 2 x + 5 (3 x) + 5 \cdot 15 = - 3$

$y = 3 x + 15$

Multiply $3$ by $5$ .

$- 2 x + 15 x + 5 \cdot 15 = - 3$

$y = 3 x + 15$

Multiply $5$ by $15$ .

$- 2 x + 15 x + 75 = - 3$

$y = 3 x + 15$

$- 2 x + 15 x + 75 = - 3$

$y = 3 x + 15$

Add $- 2 x$ and $15 x$ .

$13 x + 75 = - 3$

$y = 3 x + 15$

$13 x + 75 = - 3$

$y = 3 x + 15$

$13 x + 75 = - 3$

$y = 3 x + 15$

$13 x + 75 = - 3$

$y = 3 x + 15$

Step 3

Solve for $x$ in $13 x + 75 = - 3$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $75$ from both sides of the equation.

$13 x = - 3 - 75$

$y = 3 x + 15$

Subtract $75$ from $- 3$ .

$13 x = - 78$

$y = 3 x + 15$

$13 x = - 78$

$y = 3 x + 15$

Divide each term in $13 x = - 78$ by $13$ and simplify.

Divide each term in $13 x = - 78$ by $13$ .

$\frac{13 x}{13} = \frac{- 78}{13}$

$y = 3 x + 15$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{- 78}{13}$

$y = 3 x + 15$

Divide $x$ by $1$ .

$x = \frac{- 78}{13}$

$y = 3 x + 15$

$x = \frac{- 78}{13}$

$y = 3 x + 15$

$x = \frac{- 78}{13}$

$y = 3 x + 15$

Simplify the right side.

Divide $- 78$ by $13$ .

$x = - 6$

$y = 3 x + 15$

$x = - 6$

$y = 3 x + 15$

$x = - 6$

$y = 3 x + 15$

$x = - 6$

$y = 3 x + 15$

Step 4

Replace all occurrences of $x$ with $- 6$ in each equation.

Replace all occurrences of $x$ in $y = 3 x + 15$ with $- 6$ .

$y = 3 (- 6) + 15$

$x = - 6$

Simplify the right side.

Simplify $3 (- 6) + 15$ .

Multiply $3$ by $- 6$ .

$y = - 18 + 15$

$x = - 6$

Add $- 18$ and $15$ .

$y = - 3$

$x = - 6$

$y = - 3$

$x = - 6$

$y = - 3$

$x = - 6$

$y = - 3$

$x = - 6$

Step 5

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

$(- 6, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, - 3)$

Equation Form:

$x = - 6, y = - 3$

Step 7

Solve the System of Equations y-15=3x -2x+5y=-3

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