Solve the System of Equations 2a-3c=-6 a+2c=11

$2 a - 3 c = - 6$ $a + 2 c = 11$

Step 1

Subtract $2 c$ from both sides of the equation.

$a = 11 - 2 c$

$2 a - 3 c = - 6$

Step 2

Replace all occurrences of $a$ with $11 - 2 c$ in each equation.

Replace all occurrences of $a$ in $2 a - 3 c = - 6$ with $11 - 2 c$ .

$2 (11 - 2 c) - 3 c = - 6$

$a = 11 - 2 c$

Simplify the left side.

Simplify $2 (11 - 2 c) - 3 c$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 11 + 2 (- 2 c) - 3 c = - 6$

$a = 11 - 2 c$

Multiply $2$ by $11$ .

$22 + 2 (- 2 c) - 3 c = - 6$

$a = 11 - 2 c$

Multiply $- 2$ by $2$ .

$22 - 4 c - 3 c = - 6$

$a = 11 - 2 c$

$22 - 4 c - 3 c = - 6$

$a = 11 - 2 c$

Subtract $3 c$ from $- 4 c$ .

$22 - 7 c = - 6$

$a = 11 - 2 c$

$22 - 7 c = - 6$

$a = 11 - 2 c$

$22 - 7 c = - 6$

$a = 11 - 2 c$

$22 - 7 c = - 6$

$a = 11 - 2 c$

Step 3

Solve for $c$ in $22 - 7 c = - 6$ .

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

Subtract $22$ from both sides of the equation.

$- 7 c = - 6 - 22$

$a = 11 - 2 c$

Subtract $22$ from $- 6$ .

$- 7 c = - 28$

$a = 11 - 2 c$

$- 7 c = - 28$

$a = 11 - 2 c$

Divide each term in $- 7 c = - 28$ by $- 7$ and simplify.

Divide each term in $- 7 c = - 28$ by $- 7$ .

$\frac{- 7 c}{- 7} = \frac{- 28}{- 7}$

$a = 11 - 2 c$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 c}{- 7} = \frac{- 28}{- 7}$

$a = 11 - 2 c$

Divide $c$ by $1$ .

$c = \frac{- 28}{- 7}$

$a = 11 - 2 c$

$c = \frac{- 28}{- 7}$

$a = 11 - 2 c$

$c = \frac{- 28}{- 7}$

$a = 11 - 2 c$

Simplify the right side.

Divide $- 28$ by $- 7$ .

$c = 4$

$a = 11 - 2 c$

$c = 4$

$a = 11 - 2 c$

$c = 4$

$a = 11 - 2 c$

$c = 4$

$a = 11 - 2 c$

Step 4

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

Replace all occurrences of $c$ in $a = 11 - 2 c$ with $4$ .

$a = 11 - 2 \cdot 4$

$c = 4$

Simplify the right side.

Simplify $11 - 2 \cdot 4$ .

Multiply $- 2$ by $4$ .

$a = 11 - 8$

$c = 4$

Subtract $8$ from $11$ .

$a = 3$

$c = 4$

$a = 3$

$c = 4$

$a = 3$

$c = 4$

$a = 3$

$c = 4$

Step 5

List all of the solutions.

$a = 3, c = 4$

Solve the System of Equations 2a-3c=-6 a+2c=11

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