SOLUTION: what multiplier should be used for each of the following equations to eliminate one unknown by subtraction? 3x-y=7 2x+7y=42

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Question 252508: what multiplier should be used for each of the following equations to eliminate one unknown by subtraction?
3x-y=7
2x+7y=42
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The multiplier is 7 since this will change -y into -7y. Add this to 7y to get -7+7y=0y=0 which means that it cancels out.




Start with the given system of equations:
system%283x-y=7%2C2x%2B7y=42%29


7%283x-y%29=7%287%29 Multiply the both sides of the first equation by 7.


21x-7y=49 Distribute and multiply.


So we have the new system of equations:
system%2821x-7y=49%2C2x%2B7y=42%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:


%2821x-7y%29%2B%282x%2B7y%29=%2849%29%2B%2842%29


%2821x%2B2x%29%2B%28-7y%2B7y%29=49%2B42 Group like terms.


23x%2B0y=91 Combine like terms.


23x=91 Simplify.


x=%2891%29%2F%2823%29 Divide both sides by 23 to isolate x.


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21x-7y=49 Now go back to the first equation.


21%2891%2F23%29-7y=49 Plug in x=91%2F23.


1911%2F23-7y=49 Multiply.


23%281911%2Fcross%2823%29-7y%29=23%2849%29 Multiply both sides by the LCD 23 to clear any fractions.


1911-161y=1127 Distribute and multiply.


-161y=1127-1911 Subtract 1911 from both sides.


-161y=-784 Combine like terms on the right side.


y=%28-784%29%2F%28-161%29 Divide both sides by -161 to isolate y.


y=112%2F23 Reduce.


So the solutions are x=91%2F23 and y=112%2F23.


Which form the ordered pair .


This means that the system is consistent and independent.