Given x + y = 3k and 4x - 6k = 2y, which of the following is equal to x? a. 2y b. y c. 2k d. k e. k/2

Here are two ways to solve

Method 1: Elimination

x+y = 3k ... start with the first equation
4x+4y = 12k ... multiply every term by 4 
4x-6k = 2y ... move onto the second equation
4x-2y = 6k ... subtract 2y from both sides and add 6k to both sides

The system of equations turns into
4x+4y = 12k
4x-2y = 6k

which, when subtracted, leads to 0x+6y = 6k so y = k when you divide both sides by 6

Use y = k to find x
x+y = 3k
x+k = 3k
x = 2k

The answer is 2k



Method 2: Substitution

x+y = 3k ... start with the first equation
y = -x+3k ... isolate y; subtract x from both sides
4x-6k = 2y ... move onto the second equation
4x-6k = 2(-x+3k) ... plug in y = -x+3k; solve for x
4x-6k = -2x+6k
4x+2x = 6k+6k
6x = 12k
x = 12k/6
x = 2k



Whichever method you use, the answer is x = 2k