In order to solve the following system of equations by elimination, which process creates opposite coefficients to eliminate the y variable?
2x + y = 5
x + 4y = −7
A. Multiply the first equation by 4*******
B. Multiply the second equation by 2
C. Multiply the first equation by -4
D. Multiply the second equation by -2
A??? IDK PLZ HELPP
I am going with A!
It’s C
I would say either A or C depending on if you add or subtract the resulting equations. If your text adds, then C
it said " .... creates opposite coefficients to eliminate the y"
so clearly C
To solve the given system of equations by elimination, we want to create opposite coefficients for the y variable so that when we add or subtract the equations, the y variable will cancel out.
Looking at the two equations:
2x + y = 5
x + 4y = -7
If we multiply the first equation by 4, we get:
(4)(2x + y) = (4)(5)
8x + 4y = 20
Now, if we compare the second equation, x + 4y = -7, with the new equation we obtained, 8x + 4y = 20, we see that the coefficients of the y variable have become opposite. The coefficient(s) of y in the two equations are now 4y and -4y, which can be eliminated by adding or subtracting the equations.
Therefore, the correct process to create opposite coefficients and eliminate the y variable is to multiply the first equation by 4.
Hence, the answer is A. Multiply the first equation by 4.