SOLUTION: Solve the equations for x and y or state that there is no solution. x + y = 4 2x + 3y = -7

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Question 183042: Solve the equations for x and y or state that
there is no solution.
x + y = 4
2x + 3y = -7

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%2By=4%2C2x%2B3y=-7%29


-2%28x%2By%29=-2%284%29 Multiply the both sides of the first equation by -2.


-2x-2y=-8 Distribute and multiply.


So we have the new system of equations:
system%28-2x-2y=-8%2C2x%2B3y=-7%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:


%28-2x-2y%29%2B%282x%2B3y%29=%28-8%29%2B%28-7%29


%28-2x%2B2x%29%2B%28-2y%2B3y%29=-8%2B-7 Group like terms.


0x%2By=-15 Combine like terms.


y=-15 Simplify.


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-2x-2y=-8 Now go back to the first equation.


-2x-2%28-15%29=-8 Plug in y=-15.


-2x%2B30=-8 Multiply.


-2x=-8-30 Subtract 30 from both sides.


-2x=-38 Combine like terms on the right side.


x=%28-38%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=19 Reduce.


So our answer is x=19 and y=-15.


Which form the ordered pair .


This means that the system is consistent and independent.