Final answer:
To cancel out the x term in the given system of equations, option C should be used: multiply the first equation by -5 and the second by 4. This results in identical coefficients for x in opposite signs, allowing them to be cancelled out when added together.
Step-by-step explanation:
To solve the system of equations given by 4x+8y=-4 and -5x+3y=-21 and get the x terms to cancel out, you would use option C) Multiply the top equation by -5 and the bottom equation by 4. By doing this, the x coefficients become +20x and -20x, respectively, which will cancel out when you add the two equations together.
Multiplying the first equation by -5 yields -20x - 40y = 20, and multiplying the second equation by 4 gives us -20x + 12y = -84. Now, when we add both equations, -20x cancels out, and we simply combine the y terms and constants:
-20x - 40y + 20x + 12y = 20 - 84
-28y = -64
y = -64 / -28
y = 64 / 28
y = 16 / 7 or approximately 2.286