To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 2x − 4y = 6 −3x + 3y = 12 a) add 3 times the second equation to 4 times the first equation b) add 4 times the second equation to 3 times the first equation c) subtract 3 times the second equation from 4 times the first equation d) subtract 4 times the second equation from 3 times the first equation

Option B is correct.

add 4 times the second equation to 3 times the first equation

Step-by-step explanation:

Given the system of equation:

                        ......[1]

                      .....[2]

Multiply equation [1] by 3 we get;

Using distributive property;

6x - 12y = 18                                   .......[3]

Multiply equation [2] by 4 we get;

Using distributive property we get;

-12x + 12y = 48                                   ......[4]

Add equation [3] and [4] to eliminate y and solve for x;

(6x -12y) + ( -12x +12y ) = 18 + 48

6x - 12y -12x + 12y = 66

Combine like terms;

6x - 12x = 66

or

-6x = 66

Simplify:

x = -11

Therefore, the operation which could be used to eliminate the y-variable and find the value of x is;

add 4 times the second equation to 3 times the first equation.