Question 572164: How do you solve this system by using the elimination method?
{2x-y=20
{3x+2y=-19
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website! 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!
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