Solve the System of Equations 5a+5b+5c=-20 4a+3b+3c=-6 -4a+3b+3c=9

$5 a + 5 b + 5 c = - 20$ $4 a + 3 b + 3 c = - 6$ $- 4 a + 3 b + 3 c = 9$

Solve for $a$ in $5 a + 5 b + 5 c = - 20$ .

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

Subtract $5 b$ from both sides of the equation.

$5 a + 5 c = - 20 - 5 b$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Subtract $5 c$ from both sides of the equation.

$5 a = - 20 - 5 b - 5 c$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$5 a = - 20 - 5 b - 5 c$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Divide each term in $5 a = - 20 - 5 b - 5 c$ by $5$ and simplify.

Divide each term in $5 a = - 20 - 5 b - 5 c$ by $5$ .

$\frac{5 a}{5} = \frac{- 20}{5} + \frac{- 5 b}{5} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 a}{5} = \frac{- 20}{5} + \frac{- 5 b}{5} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Divide $a$ by $1$ .

$a = \frac{- 20}{5} + \frac{- 5 b}{5} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = \frac{- 20}{5} + \frac{- 5 b}{5} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = \frac{- 20}{5} + \frac{- 5 b}{5} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Simplify the right side.

Simplify each term.

Divide $- 20$ by $5$ .

$a = - 4 + \frac{- 5 b}{5} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Cancel the common factor of $- 5$ and $5$ .

Factor $5$ out of $- 5 b$ .

$a = - 4 + \frac{5 (- b)}{5} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Cancel the common factors.

Factor $5$ out of $5$ .

$a = - 4 + \frac{5 (- b)}{5 (1)} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Cancel the common factor.

$a = - 4 + \frac{5 (- b)}{5 \cdot 1} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Rewrite the expression.

$a = - 4 + \frac{- b}{1} + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Divide $- b$ by $1$ .

$a = - 4 - b + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = - 4 - b + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = - 4 - b + \frac{- 5 c}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Cancel the common factor of $- 5$ and $5$ .

Factor $5$ out of $- 5 c$ .

$a = - 4 - b + \frac{5 (- c)}{5}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Cancel the common factors.

Factor $5$ out of $5$ .

$a = - 4 - b + \frac{5 (- c)}{5 (1)}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Cancel the common factor.

$a = - 4 - b + \frac{5 (- c)}{5 \cdot 1}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Rewrite the expression.

$a = - 4 - b + \frac{- c}{1}$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Divide $- c$ by $1$ .

$a = - 4 - b - c$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = - 4 - b - c$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = - 4 - b - c$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = - 4 - b - c$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = - 4 - b - c$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = - 4 - b - c$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

$a = - 4 - b - c$

$4 a + 3 b + 3 c = - 6$

$- 4 a + 3 b + 3 c = 9$

Replace all occurrences of $a$ with $- 4 - b - c$ in each equation.

Replace all occurrences of $a$ in $4 a + 3 b + 3 c = - 6$ with $- 4 - b - c$ .

$4 (- 4 - b - c) + 3 b + 3 c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

Simplify the left side.

Simplify $4 (- 4 - b - c) + 3 b + 3 c$ .

Simplify each term.

Apply the distributive property.

$4 \cdot - 4 + 4 (- b) + 4 (- c) + 3 b + 3 c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

Simplify.

Multiply $4$ by $- 4$ .

$- 16 + 4 (- b) + 4 (- c) + 3 b + 3 c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

Multiply $- 1$ by $4$ .

$- 16 - 4 b + 4 (- c) + 3 b + 3 c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

Multiply $- 1$ by $4$ .

$- 16 - 4 b - 4 c + 3 b + 3 c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

$- 16 - 4 b - 4 c + 3 b + 3 c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

$- 16 - 4 b - 4 c + 3 b + 3 c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

Simplify by adding terms.

Add $- 4 b$ and $3 b$ .

$- 16 - b - 4 c + 3 c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

Add $- 4 c$ and $3 c$ .

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$- 4 a + 3 b + 3 c = 9$

Replace all occurrences of $a$ in $- 4 a + 3 b + 3 c = 9$ with $- 4 - b - c$ .

$- 4 (- 4 - b - c) + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Simplify the left side.

Simplify $- 4 (- 4 - b - c) + 3 b + 3 c$ .

Simplify each term.

Apply the distributive property.

$- 4 \cdot - 4 - 4 (- b) - 4 (- c) + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Simplify.

Multiply $- 4$ by $- 4$ .

$16 - 4 (- b) - 4 (- c) + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Multiply $- 1$ by $- 4$ .

$16 + 4 b - 4 (- c) + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Multiply $- 1$ by $- 4$ .

$16 + 4 b + 4 c + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$16 + 4 b + 4 c + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$16 + 4 b + 4 c + 3 b + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Simplify by adding terms.

Add $4 b$ and $3 b$ .

$16 + 7 b + 4 c + 3 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Add $4 c$ and $3 c$ .

$16 + 7 b + 7 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$16 + 7 b + 7 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$16 + 7 b + 7 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$16 + 7 b + 7 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$16 + 7 b + 7 c = 9$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Solve for $b$ in $16 + 7 b + 7 c = 9$ .

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

Subtract $16$ from both sides of the equation.

$7 b + 7 c = 9 - 16$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Subtract $7 c$ from both sides of the equation.

$7 b = 9 - 16 - 7 c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Subtract $16$ from $9$ .

$7 b = - 7 - 7 c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$7 b = - 7 - 7 c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Divide each term in $7 b = - 7 - 7 c$ by $7$ and simplify.

Divide each term in $7 b = - 7 - 7 c$ by $7$ .

$\frac{7 b}{7} = \frac{- 7}{7} + \frac{- 7 c}{7}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 b}{7} = \frac{- 7}{7} + \frac{- 7 c}{7}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Divide $b$ by $1$ .

$b = \frac{- 7}{7} + \frac{- 7 c}{7}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$b = \frac{- 7}{7} + \frac{- 7 c}{7}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$b = \frac{- 7}{7} + \frac{- 7 c}{7}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Simplify the right side.

Simplify each term.

Divide $- 7$ by $7$ .

$b = - 1 + \frac{- 7 c}{7}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Cancel the common factor of $- 7$ and $7$ .

Factor $7$ out of $- 7 c$ .

$b = - 1 + \frac{7 (- c)}{7}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Cancel the common factors.

Factor $7$ out of $7$ .

$b = - 1 + \frac{7 (- c)}{7 (1)}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Cancel the common factor.

$b = - 1 + \frac{7 (- c)}{7 \cdot 1}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Rewrite the expression.

$b = - 1 + \frac{- c}{1}$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Divide $- c$ by $1$ .

$b = - 1 - c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$b = - 1 - c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$b = - 1 - c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$b = - 1 - c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$b = - 1 - c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$b = - 1 - c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

$b = - 1 - c$

$- 16 - b - c = - 6$

$a = - 4 - b - c$

Replace all occurrences of $b$ with $- 1 - c$ in each equation.

Replace all occurrences of $b$ in $- 16 - b - c = - 6$ with $- 1 - c$ .

$- 16 - (- 1 - c) - c = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

Simplify the left side.

Simplify $- 16 - (- 1 - c) - c$ .

Simplify each term.

Apply the distributive property.

$- 16 + 1 + c - c = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

Multiply $- 1$ by $- 1$ .

$- 16 + 1 + c - c = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

Multiply $- - c$ .

Multiply $- 1$ by $- 1$ .

$- 16 + 1 + 1 c - c = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

Multiply $c$ by $1$ .

$- 16 + 1 + c - c = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

$- 16 + 1 + c - c = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

$- 16 + 1 + c - c = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

Simplify by adding terms.

Combine the opposite terms in $- 16 + 1 + c - c$ .

Subtract $c$ from $c$ .

$- 16 + 1 + 0 = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

Add $- 16 + 1$ and $0$ .

$- 16 + 1 = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

$- 16 + 1 = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

Add $- 16$ and $1$ .

$- 15 = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

$- 15 = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

$- 15 = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

$- 15 = - 6$

$b = - 1 - c$

$a = - 4 - b - c$

Replace all occurrences of $b$ in $a = - 4 - b - c$ with $- 1 - c$ .

$a = - 4 - (- 1 - c) - c$

$- 15 = - 6$

$b = - 1 - c$

Simplify the right side.

Simplify $- 4 - (- 1 - c) - c$ .

Simplify each term.

Apply the distributive property.

$a = - 4 + 1 + c - c$

$- 15 = - 6$

$b = - 1 - c$

Multiply $- 1$ by $- 1$ .

$a = - 4 + 1 + c - c$

$- 15 = - 6$

$b = - 1 - c$

Multiply $- - c$ .

Multiply $- 1$ by $- 1$ .

$a = - 4 + 1 + 1 c - c$

$- 15 = - 6$

$b = - 1 - c$

Multiply $c$ by $1$ .

$a = - 4 + 1 + c - c$

$- 15 = - 6$

$b = - 1 - c$

$a = - 4 + 1 + c - c$

$- 15 = - 6$

$b = - 1 - c$

$a = - 4 + 1 + c - c$

$- 15 = - 6$

$b = - 1 - c$

Simplify by adding terms.

Combine the opposite terms in $- 4 + 1 + c - c$ .

Subtract $c$ from $c$ .

$a = - 4 + 1 + 0$

$- 15 = - 6$

$b = - 1 - c$

Add $- 4 + 1$ and $0$ .

$a = - 4 + 1$

$- 15 = - 6$

$b = - 1 - c$

$a = - 4 + 1$

$- 15 = - 6$

$b = - 1 - c$

Add $- 4$ and $1$ .

$a = - 3$

$- 15 = - 6$

$b = - 1 - c$

$a = - 3$

$- 15 = - 6$

$b = - 1 - c$

$a = - 3$

$- 15 = - 6$

$b = - 1 - c$

$a = - 3$

$- 15 = - 6$

$b = - 1 - c$

$a = - 3$

$- 15 = - 6$

$b = - 1 - c$

Since $- 15 = - 6$ is not true, there is no solution.

No solution

Solve the System of Equations 5a+5b+5c=-20 4a+3b+3c=-6 -4a+3b+3c=9

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