Solve the System of Equations -2a+3b=14 a-4b=3

$- 2 a + 3 b = 14$ $a - 4 b = 3$

Step 1

Add $4 b$ to both sides of the equation.

$a = 3 + 4 b$

$- 2 a + 3 b = 14$

Step 2

Replace all occurrences of $a$ with $3 + 4 b$ in each equation.

Replace all occurrences of $a$ in $- 2 a + 3 b = 14$ with $3 + 4 b$ .

$- 2 (3 + 4 b) + 3 b = 14$

$a = 3 + 4 b$

Simplify the left side.

Simplify $- 2 (3 + 4 b) + 3 b$ .

Simplify each term.

Apply the distributive property.

$- 2 \cdot 3 - 2 (4 b) + 3 b = 14$

$a = 3 + 4 b$

Multiply $- 2$ by $3$ .

$- 6 - 2 (4 b) + 3 b = 14$

$a = 3 + 4 b$

Multiply $4$ by $- 2$ .

$- 6 - 8 b + 3 b = 14$

$a = 3 + 4 b$

$- 6 - 8 b + 3 b = 14$

$a = 3 + 4 b$

Add $- 8 b$ and $3 b$ .

$- 6 - 5 b = 14$

$a = 3 + 4 b$

$- 6 - 5 b = 14$

$a = 3 + 4 b$

$- 6 - 5 b = 14$

$a = 3 + 4 b$

$- 6 - 5 b = 14$

$a = 3 + 4 b$

Step 3

Solve for $b$ in $- 6 - 5 b = 14$ .

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

Add $6$ to both sides of the equation.

$- 5 b = 14 + 6$

$a = 3 + 4 b$

Add $14$ and $6$ .

$- 5 b = 20$

$a = 3 + 4 b$

$- 5 b = 20$

$a = 3 + 4 b$

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

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

$\frac{- 5 b}{- 5} = \frac{20}{- 5}$

$a = 3 + 4 b$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 b}{- 5} = \frac{20}{- 5}$

$a = 3 + 4 b$

Divide $b$ by $1$ .

$b = \frac{20}{- 5}$

$a = 3 + 4 b$

$b = \frac{20}{- 5}$

$a = 3 + 4 b$

$b = \frac{20}{- 5}$

$a = 3 + 4 b$

Simplify the right side.

Divide $20$ by $- 5$ .

$b = - 4$

$a = 3 + 4 b$

$b = - 4$

$a = 3 + 4 b$

$b = - 4$

$a = 3 + 4 b$

$b = - 4$

$a = 3 + 4 b$

Step 4

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

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

$a = 3 + 4 (- 4)$

$b = - 4$

Simplify the right side.

Simplify $3 + 4 (- 4)$ .

Multiply $4$ by $- 4$ .

$a = 3 - 16$

$b = - 4$

Subtract $16$ from $3$ .

$a = - 13$

$b = - 4$

$a = - 13$

$b = - 4$

$a = - 13$

$b = - 4$

$a = - 13$

$b = - 4$

Step 5

List all of the solutions.

$a = - 13, b = - 4$

Solve the System of Equations -2a+3b=14 a-4b=3

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