Manny says he should multiply the first equation in the system of equations below by 3 and the second equation by 2, then add to eliminate the x-terms. Is there a more effective way to solve this system? Explain your answer.
−2x+y=15
3x+4y=−12
(1 point)
Responses
Yes, a more efficient way is to multiply the first equation by 4, add to eliminate y, then solve for x.
Yes, a more efficient way is to multiply the first equation by 4, add to eliminate y, then solve for x.
Yes, a more efficient way is to multiply the first equation by -4, add to eliminate y, then solve for x.
Yes, a more efficient way is to multiply the first equation by -4, add to eliminate y, then solve for x.
No, there isn't a more efficient way to solve this system.
No, there isn't a more efficient way to solve this system.
Yes, a more efficient way is to multiply the first equation by -4, add to eliminate x, then solve for y.
No, there isn't a more efficient way to solve this system.
The method suggested by Manny of multiplying the first equation by 3 and the second equation by 2, then adding to eliminate the x-terms is the most efficient way to solve this system. This will give us an equation with only the y-term, which can then be solved for y. Once y is found, we can substitute it back into one of the original equations to solve for x. This method avoids unnecessary calculations and simplification steps.