Question

solve the system by the method of your choice.$\frac{x}{2}-\frac{y}{2}=-1$$x + 2y = -14$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: Simplify first equation

Multiply both sides by 2:
$$\frac{x}{2} \times 2 - \frac{y}{2} \times 2 = -1 \times 2$$
$$x - y = -2$$

Step2: Isolate $x$ from simplified eq

Rearrange to solve for $x$:
$$x = y - 2$$

Step3: Substitute $x$ into second eq

Replace $x$ in $x + 2y = -14$:
$$(y - 2) + 2y = -14$$

Step4: Solve for $y$

Combine like terms and isolate $y$:
$$3y - 2 = -14$$
$$3y = -14 + 2 = -12$$
$$y = \frac{-12}{3} = -4$$

Step5: Find $x$ using $y=-4$

Substitute $y=-4$ into $x = y - 2$:
$$x = -4 - 2 = -6$$

Answer:

A. The solution set is $\boldsymbol{(-6, -4)}$