identify the solution (s) of the system of equations, if any.

-3x-4y=2
8y=-6x-4

a. infinitely many solutions
b. (-16/9, 5/6)
c.(-2/3,0)
d. no solution

a is correct answer

4y=-3x-2

8y=-6x-2 from the first equation, setting it equal to the second.

-6x-2=-6x-4
-2=-6 Hmmm No solution. The lines are parallel

To identify the solution(s) of the system of equations, we can use different methods such as substitution, elimination, or graphing. In this case, let's use the method of substitution.

We have the following system of equations:

Equation 1: -3x - 4y = 2
Equation 2: 8y = -6x - 4

From Equation 2, let's solve for y:

8y = -6x - 4
Divide both sides by 8:
y = (-6x - 4)/8
y = (-3/4)x - 1/2

Now, let's substitute the value of y from Equation 2 into Equation 1:

-3x - 4((-3/4)x - 1/2) = 2
Simplify:
-3x + 3x + 2 = 2
2 = 2

Since the equation simplifies to a true statement (2 = 2), it means that the two equations are equivalent, and their graphs will overlap. This implies that the system has infinitely many solutions.

Therefore, the solution to the system of equations is:

a. Infinitely many solutions