SOLUTION: Solve the following system of equations algebraically: 3x+2y=4 4x+3y=7

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Question 252597: Solve the following system of equations algebraically:
3x+2y=4
4x+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%283x%2B2y=4%2C4x%2B3y=7%29


3%283x%2B2y%29=3%284%29 Multiply the both sides of the first equation by 3.


9x%2B6y=12 Distribute and multiply.


-2%284x%2B3y%29=-2%287%29 Multiply the both sides of the second equation by -2.


-8x-6y=-14 Distribute and multiply.


So we have the new system of equations:
system%289x%2B6y=12%2C-8x-6y=-14%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:


%289x%2B6y%29%2B%28-8x-6y%29=%2812%29%2B%28-14%29


%289x%2B-8x%29%2B%286y%2B-6y%29=12%2B-14 Group like terms.


x%2B0y=-2 Combine like terms.


x=-2 Simplify.


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9x%2B6y=12 Now go back to the first equation.


9%28-2%29%2B6y=12 Plug in x=-2.


-18%2B6y=12 Multiply.


6y=12%2B18 Add 18 to both sides.


6y=30 Combine like terms on the right side.


y=%2830%29%2F%286%29 Divide both sides by 6 to isolate y.


y=5 Reduce.


So the solutions are x=-2 and y=5.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 3x%2B2y=4 (red) and 4x%2B3y=7 (green)