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how do I solve 1/2x+3/5y=17
1/5x+3/4y=17
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= , (1)
= . (2)
First of all, multiply the equation (1) by 10 (both sides) and the equation (2) by 20 to get off the denominators. You will get an equivalent system
5x + 6y = 170, (3)
4x + 15y = 340. (4)
Next multiply the equation (3) by 4 (both sides) and the equation (4) by (-5) and then add.
By doing this way, you eliminate x and obtain a single equation for y:
24y - 75y = 4*170 - 5*340, or
-51y = -1020.
Hence y = = 20.
Now substitute the found value y = 20 into the equation (3) and find x = 10.