SOLUTION: 2x-5y=-14 4x-3y=8 State exact values. If the system is dependent, express the solution set in terms of one of

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Question 201584: 2x-5y=-14 4x-3y=8 State exact values. If the system is dependent, express the solution set in terms of one of the variables
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%282x-5y=-14%2C4x-3y=8%29


-2%282x-5y%29=-2%28-14%29 Multiply the both sides of the first equation by -2.


-4x%2B10y=28 Distribute and multiply.


So we have the new system of equations:
system%28-4x%2B10y=28%2C4x-3y=8%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:


%28-4x%2B10y%29%2B%284x-3y%29=%2828%29%2B%288%29


%28-4x%2B4x%29%2B%2810y%2B-3y%29=28%2B8 Group like terms.


0x%2B7y=36 Combine like terms.


7y=36 Simplify.


y=%2836%29%2F%287%29 Divide both sides by 7 to isolate y.


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-4x%2B10y=28 Now go back to the first equation.


-4x%2B10%2836%2F7%29=28 Plug in y=36%2F7.


-4x%2B360%2F7=28 Multiply.


7%28-4x%2B360%2Fcross%287%29%29=7%2828%29 Multiply both sides by the LCD 7 to clear any fractions.


-28x%2B360=196 Distribute and multiply.


-28x=196-360 Subtract 360 from both sides.


-28x=-164 Combine like terms on the right side.


x=%28-164%29%2F%28-28%29 Divide both sides by -28 to isolate x.


x=41%2F7 Reduce.


So the solutions are x=41%2F7 and y=36%2F7.


Which form the ordered pair .


This means that the system is consistent and independent.