SOLUTION: how do i eliminate x+5y=17 -4x-3y=24 ?

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Question 171367This question is from textbook
: how do i eliminate x+5y=17 -4x-3y=24 ?
 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%28x%2B5y=17%2C-4x-3y=24%29


4%28x%2B5y%29=4%2817%29 Multiply the both sides of the first equation by 4. This will make the "x" coefficients equal but opposite (which will mean that they will cancel).


4x%2B20y=68 Distribute and multiply.


So we have the new system of equations:
system%284x%2B20y=68%2C-4x-3y=24%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:


%284x%2B20y%29%2B%28-4x-3y%29=%2868%29%2B%2824%29


%284x%2B-4x%29%2B%2820y%2B-3y%29=68%2B24 Group like terms.


0x%2B17y=92 Combine like terms. Notice how the x terms cancel out.


17y=92 Simplify.


y=%2892%29%2F%2817%29 Divide both sides by 17 to isolate y.


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4x%2B20y=68 Now go back to the first equation.


4x%2B20%2892%2F17%29=68 Plug in y=92%2F17.


4x%2B1840%2F17=68 Multiply.


17%284x%29%2Bcross%2817%29%281840%2Fcross%2817%29%29=17%2868%29 Multiply EVERY term by the LCD 17 to clear any fractions.


68x%2B1840=1156 Distribute and multiply.


68x=1156-1840 Subtract 1840 from both sides.


68x=-684 Combine like terms on the right side.


x=%28-684%29%2F%2868%29 Divide both sides by 68 to isolate x.


x=-171%2F17 Reduce.


So the solutions are x=-171%2F17 and y=92%2F17.


Which form the ordered pair .


This means that the system is consistent and independent.