SOLUTION: Back again with some homework! I'm stuck on two problems in one section, ive been able to do the questions up until this question particularly: find each system as consistent d

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Back again with some homework! I'm stuck on two problems in one section, ive been able to do the questions up until this question particularly: find each system as consistent d      Log On


   

Question 191410This question is from textbook algebra 1
: Back again with some homework!
I'm stuck on two problems in one section, ive been able to do the questions up until this question particularly:
find each system as consistent dependent or consistent independent, or inconsistent
{ 2x-3/4y=17
{ -3x-5/8y=-11
i tried using elimination to find the answer but nothing i get seems right. if someone could explain HOW to solve it it would be a major major help! This question is from textbook algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x-%283%2F4%29y=17 Start with the first equation.


4%282x%29-cross%284%29%28%283%2Fcross%284%29%29y%29=4%2817%29 Multiply EVERY term by the LCD 4 to clear any fractions.


8x-3y=68 Multiply.


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-3x-%285%2F8%29y=-11+ Move onto the second equation.


8%28-3x%29-cross%288%29%28%285%2Fcross%288%29%29y%29=8%28-11%29 Multiply EVERY term by the LCD 8 to clear any fractions.


-24x-5y=-88 Multiply.


So we have the system of equations:


system%288x-3y=68%2C-24x-5y=-88%29



3%288x-3y%29=3%2868%29 Multiply the both sides of the first equation by 3.


24x-9y=204 Distribute and multiply.


So we have the new system of equations:
system%2824x-9y=204%2C-24x-5y=-88%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%2824x-9y%29%2B%28-24x-5y%29=%28204%29%2B%28-88%29


%2824x%2B-24x%29%2B%28-9y%2B-5y%29=204%2B-88 Group like terms.


0x%2B-14y=116 Combine like terms.


-14y=116 Simplify.


y=%28116%29%2F%28-14%29 Divide both sides by -14 to isolate y.


y=-58%2F7 Reduce.


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24x-9y=204 Now go back to the first equation.


24x-9%28-58%2F7%29=204 Plug in y=-58%2F7.


24x%2B522%2F7=204 Multiply.


7%2824x%29%2Bcross%287%29%28522%2Fcross%287%29%29=7%28204%29 Multiply EVERY term by the LCD 7 to clear any fractions.


168x%2B522=1428 Multiply.


168x=1428-522 Subtract 522 from both sides.


168x=906 Combine like terms on the right side.


x=%28906%29%2F%28168%29 Divide both sides by 168 to isolate x.


x=151%2F28 Reduce.


So the solutions are x=151%2F28 and y=-58%2F7.


Which form the ordered pair .


This means that the system is consistent and independent.