Question

solve the system by the addition method.
$3x - 2y = -3$
$4x + 5y = -4$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}. (type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Eliminate y variable

Multiply first equation by 5: $5(3x - 2y) = 5(-3) \implies 15x - 10y = -15$
Multiply second equation by 2: $2(4x + 5y) = 2(-4) \implies 8x + 10y = -8$
Add the two new equations:
$$(15x - 10y) + (8x + 10y) = -15 + (-8)$$
$$23x = -23$$

Step2: Solve for x

Divide both sides by 23:
$$x = \frac{-23}{23} = -1$$

Step3: Substitute x to find y

Substitute $x=-1$ into $3x - 2y = -3$:
$$3(-1) - 2y = -3$$
$$-3 - 2y = -3$$
Add 3 to both sides: $-2y = 0$
Divide by -2: $y = 0$

Answer:

A. The solution set is $\{(-1, 0)\}$