Question 572164
2x - y  = 20
3x + 2y = -19

With the elimination method, we want to add down the columns so one of factors cancels out.  I'm going to pick y to "eliminate" here.  One y is already negative and the other positive.  That helps.  All I need to do then is make their multipliers the same.  So I'm going to multiply the whole first equation by 2 to give y its 2 factor.  

2x - y   =20
2(2x - y) = 2(20)
4x - 2y = 40


Now let's line up the equations again with this altered (but equivalent 2nd equation)


4x - 2y = 40
3x + 2y = -19  Adding vertically (use a line under the two and add columns)
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7x      = 21   Divide both sides by 7
 x = 3


Substituting to find y in the 1st equation:
2(3)-y = 20
6 - y = 20  Subtract 6 from both sides:
-y = 14   Multiply both sides by -1
y = -14


Checking:
1st equation:
2(3) - (-14) = 20
6 + 14 = 20 Correct!


2nd equation:
3(3) + 2(-14) = -19
9 - 28 = -19
-19 = -19  Correct!