Solve the System of Equations y=-5/3x-6 2x-3y=-24

$y = - \frac{5}{3} x - 6$ $2 x - 3 y = - 24$

Step 1

Simplify each term.

Combine $x$ and $\frac{5}{3}$ .

$y = - \frac{x \cdot 5}{3} - 6$

$2 x - 3 y = - 24$

Move $5$ to the left of $x$ .

$y = - \frac{5 x}{3} - 6$

$2 x - 3 y = - 24$

$y = - \frac{5 x}{3} - 6$

$2 x - 3 y = - 24$

Step 2

Replace all occurrences of $y$ with $- \frac{5 x}{3} - 6$ in each equation.

Replace all occurrences of $y$ in $2 x - 3 y = - 24$ with $- \frac{5 x}{3} - 6$ .

$2 x - 3 (- \frac{5 x}{3} - 6) = - 24$

$y = - \frac{5 x}{3} - 6$

Simplify the left side.

Simplify $2 x - 3 (- \frac{5 x}{3} - 6)$ .

Simplify each term.

Apply the distributive property.

$2 x - 3 (- \frac{5 x}{3}) - 3 \cdot - 6 = - 24$

$y = - \frac{5 x}{3} - 6$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5 x}{3}$ into the numerator.

$2 x - 3 \frac{- 5 x}{3} - 3 \cdot - 6 = - 24$

$y = - \frac{5 x}{3} - 6$

Factor $3$ out of $- 3$ .

$2 x + 3 (- 1) (\frac{- 5 x}{3}) - 3 \cdot - 6 = - 24$

$y = - \frac{5 x}{3} - 6$

Cancel the common factor.

$2 x + 3 \cdot (- 1 \frac{- 5 x}{3}) - 3 \cdot - 6 = - 24$

$y = - \frac{5 x}{3} - 6$

Rewrite the expression.

$2 x - 1 (- 5 x) - 3 \cdot - 6 = - 24$

$y = - \frac{5 x}{3} - 6$

$2 x - 1 (- 5 x) - 3 \cdot - 6 = - 24$

$y = - \frac{5 x}{3} - 6$

Multiply $- 5$ by $- 1$ .

$2 x + 5 x - 3 \cdot - 6 = - 24$

$y = - \frac{5 x}{3} - 6$

Multiply $- 3$ by $- 6$ .

$2 x + 5 x + 18 = - 24$

$y = - \frac{5 x}{3} - 6$

$2 x + 5 x + 18 = - 24$

$y = - \frac{5 x}{3} - 6$

Add $2 x$ and $5 x$ .

$7 x + 18 = - 24$

$y = - \frac{5 x}{3} - 6$

$7 x + 18 = - 24$

$y = - \frac{5 x}{3} - 6$

$7 x + 18 = - 24$

$y = - \frac{5 x}{3} - 6$

$7 x + 18 = - 24$

$y = - \frac{5 x}{3} - 6$

Step 3

Solve for $x$ in $7 x + 18 = - 24$ .

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

Subtract $18$ from both sides of the equation.

$7 x = - 24 - 18$

$y = - \frac{5 x}{3} - 6$

Subtract $18$ from $- 24$ .

$7 x = - 42$

$y = - \frac{5 x}{3} - 6$

$7 x = - 42$

$y = - \frac{5 x}{3} - 6$

Divide each term in $7 x = - 42$ by $7$ and simplify.

Divide each term in $7 x = - 42$ by $7$ .

$\frac{7 x}{7} = \frac{- 42}{7}$

$y = - \frac{5 x}{3} - 6$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 42}{7}$

$y = - \frac{5 x}{3} - 6$

Divide $x$ by $1$ .

$x = \frac{- 42}{7}$

$y = - \frac{5 x}{3} - 6$

$x = \frac{- 42}{7}$

$y = - \frac{5 x}{3} - 6$

$x = \frac{- 42}{7}$

$y = - \frac{5 x}{3} - 6$

Simplify the right side.

Divide $- 42$ by $7$ .

$x = - 6$

$y = - \frac{5 x}{3} - 6$

$x = - 6$

$y = - \frac{5 x}{3} - 6$

$x = - 6$

$y = - \frac{5 x}{3} - 6$

$x = - 6$

$y = - \frac{5 x}{3} - 6$

Step 4

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

Replace all occurrences of $x$ in $y = - \frac{5 x}{3} - 6$ with $- 6$ .

$y = - \frac{5 (- 6)}{3} - 6$

$x = - 6$

Simplify the right side.

Simplify $- \frac{5 (- 6)}{3} - 6$ .

Simplify each term.

Cancel the common factor of $- 6$ and $3$ .

Factor $3$ out of $5 (- 6)$ .

$y = - \frac{3 (5 \cdot (- 2))}{3} - 6$

$x = - 6$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = - \frac{3 (5 \cdot (- 2))}{3 (1)} - 6$

$x = - 6$

Cancel the common factor.

$y = - \frac{3 (5 \cdot (- 2))}{3 \cdot 1} - 6$

$x = - 6$

Rewrite the expression.

$y = - \frac{5 \cdot (- 2)}{1} - 6$

$x = - 6$

Divide $5 \cdot (- 2)$ by $1$ .

$y = - (5 \cdot (- 2)) - 6$

$x = - 6$

$y = - (5 \cdot (- 2)) - 6$

$x = - 6$

$y = - (5 \cdot (- 2)) - 6$

$x = - 6$

Multiply $- (5 \cdot (- 2))$ .

Multiply $5$ by $- 2$ .

$y = 10 - 6$

$x = - 6$

Multiply $- 1$ by $- 10$ .

$y = 10 - 6$

$x = - 6$

$y = 10 - 6$

$x = - 6$

$y = 10 - 6$

$x = - 6$

Subtract $6$ from $10$ .

$y = 4$

$x = - 6$

$y = 4$

$x = - 6$

$y = 4$

$x = - 6$

$y = 4$

$x = - 6$

Step 5

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

$(- 6, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, 4)$

Equation Form:

$x = - 6, y = 4$

Step 7

Solve the System of Equations y=-5/3x-6 2x-3y=-24

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