Question

solve the system by the addition method.
$x + 4y = 3$
$4x + 3y = -1$

select the correct choice below and fill in any answer boxes present in your choice.
a. the solution set is {}. (simplify your answer. type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Eliminate x variable

Multiply first equation by -4:
$$-4(x + 4y) = -4(3) \implies -4x - 16y = -12$$

Step2: Add equations to solve for y

Add the modified equation to the second equation:
$$(-4x - 16y) + (4x + 3y) = -12 + (-1)$$
$$-13y = -13$$
$$y = \frac{-13}{-13} = 1$$

Step3: Substitute y to find x

Substitute $y=1$ into $x + 4y = 3$:
$$x + 4(1) = 3$$
$$x = 3 - 4 = -1$$

Answer:

A. The solution set is $\{(-1, 1)\}$. (Simplify your answer. Type an ordered pair.)