SOLUTION: solve the system of linear equations 7/11x -1/6y=29/33 2/5x-1/3y=4/15

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Question 107316: solve the system of linear equations
7/11x -1/6y=29/33
2/5x-1/3y=4/15
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
7x%2F11-y%2F6=29%2F33
2x%2F5-y%2F3=4%2F15
Whenever I have a fraction problem, I get rid of the denominators by multiplying by the product of the denominator or LCD, whichever's easier.
Multiply the first equation by 66, second equation by 15.
66%287x%2F11-y%2F6%29=66%2829%2F33%29
1.42x-11y=58%29
15%282x%2F5-y%2F3%29=15%284%2F15%29
2.6x-5y=4
Now use 2 to get y in terms of x.
2.6x-5y=4
6x-5y=4
6x-4=5y
6x%2F5-4%2F5=y
y=6x%2F5-4%2F5
Substitute that value for y in equation 1,
1.42x-11y=58%29
42x-11%286x%2F5-4%2F5%29=58%29
42x-66x%2F5%2B44%2F5=58%29
210x%2F5-66x%2F5%2B44%2F5=290%2F5%29 Change to same denominator.
144x%2F5=246%2F5%29
x=246%2F144
x=41%2F24Simplify to lowest terms.
Now you can find y,
y=6x%2F5-4%2F5
y=%286%2F5%29%2A%2841%2F24%29-4%2F5
y=%2841%2F20%29-16%2F20
y=5%2F4
Check your answers.
7x%2F11-y%2F6=29%2F33 Use your first equation.
%287%2F11%29%2841%2F24%29-%281%2F6%29%285%2F4%29=29%2F33
287%2F264-5%2F24=29%2F33
%2824%2F24%29%2A%28287%2F264%29-%28264%2F264%29%2A%285%2F24%29=29%2F33Change to same denominator.
6888%2F6336-1320%2F6336=29%2F33
5568%2F6336=29%2F33
%28cross%28192%29%2A29%29%2F%28cross%28192%29%2A33%29=29%2F33
29%2F33=29%2F33
True statement, good answer.
x=41/24(1.71), y=5/4(1.25)
+graph%28+300%2C+300%2C+-1%2C+4%2C+-1%2C+4%2C+6x%2F5-4%2F5%2C+42%2Ax%2F11-6%2A29%2F33%29+