Question 1007851
2x - 3y = 21
-6x + 2y = 7
Step 1: Eliminate either x or y to solve for one value. In this problem, we will eliminate x by multiplying the first equation by 3.
6x - 9y = 63
-6x + 2y = 7
Step 2: Add the two equations to eliminate x and solve for y.  We add because we want the x coefficient to become 0.
-7y = 70
y = -10
Step 3: Substitute the y value we just got into either one of the two original equations to get the x value.  I decided to use the first equation, but using the second equation will also get you the right answer.
2x - 3y = 21
2x - 3(-10) = 21
2x + 30 = 21
2x = -9
x = -4.5

Final Answer: 
x = -4.5
y = -10