Question 163056: solve by elimination:
3x+5y=4
5x+2y=9
Answer by joecbaseball(37)   (Show Source):
You can put this solution on YOUR website! Solve by elimination:
3x + 5y = 4
5x + 2y = 9
To solve by elimination, you must multiply the equations in such a way that when you add them together, one of the terms will fall out:
I will multiply the top equation by 5 and the bottom equation by (-3). This will make my first terms 15x and -15x, which will add to zero?
So, 5(3x + 5y = 4) gives me 15x + 25y = 20
And
(-3)(5x + 2y = 9) gives me -15x – 6y = -27
Now, add them down to get 19y = -7 and solve for y:
Thus y = -7/19.
NOW, take that value for y and put it into either of the initial equations to get your x value:
I will put it into the first equation:
3x + 5y = 4
3x + 5(-7/19) = 4
3x – 35/19 = 4
3x = 4 + 35/19
3x = 76/19 + 35/19 (finding a common denominator)
3x = 111/19
x = 111/19∙3
x = 111/57.
So, your answers are:
x = 111/57, y = -7/19.
You can check the answers by substituting into the other equation.
Good luck,
JoeC
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