Question

imagine that you are asked to use the elimination method to solve the system of linear equation below.if you wanted to eliminate the y-variable, what should your next step be
3x-6y=12
4x-7y=8

A. Multiply the top equation by 3 and the bottom equation by -4.
B. Multiply the top equation by -6 and the bottom equation by 7
C. Multiply the top equation by -4 and the bottom equation by 3
D. Multiply the top equation by 7 and the bottom equation by -6

Answer 1

Are there choices?

Answer 2

what r u trying to find out

Answer 3

oh i see them

Answer 4

You want to eliminate the y variable.
That means that the coefficient of the y variables must become opposites, so that when you add them, they add to zero.

You have -6y and -7y.
What do you multiply those terms to end up with two terms with opposites as coefficients?

Answer 5

Here's an approach that always works, though it may make larger numbers than strictly necessary:

for the variable you want to eliminate, multiply by the coefficient of the variable in the other equation. Do this for both equations. Now either add if the two have different signs, or subtract if they have identical signs.

Example:

\[3x + 2y = 6\]\[x+7y=2\]
To eliminate \(y\), multiply the first equation by 7 and the second by 2.
\[7*3x + 7*2y = 7*6\]\[2*x + 2*7y = 2*2\]

\[21x + 14 y = 42\]\[2x+14y=4\]

same sign for the \(y\) terms, so we subtract:
\[21x-2x + 14y-14y = 42 - 4\]\[19x=38\]
etc.

Answer 6

to clarify: you multiply the entire equation by the coefficient of the corresponding variable in the other equation...