SOLUTION: OKay we are givien two equations to solve ant the are 2x+5y=11 and -3x+8y=-1

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Question 188198: OKay we are givien two equations to solve ant the are 2x+5y=11 and -3x+8y=-1
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%2B5y=11%2C-3x%2B8y=-1%29


3%282x%2B5y%29=3%2811%29 Multiply the both sides of the first equation by 3.


6x%2B15y=33 Distribute and multiply.


2%28-3x%2B8y%29=2%28-1%29 Multiply the both sides of the second equation by 2.


-6x%2B16y=-2 Distribute and multiply.


So we have the new system of equations:
system%286x%2B15y=33%2C-6x%2B16y=-2%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:


%286x%2B15y%29%2B%28-6x%2B16y%29=%2833%29%2B%28-2%29


%286x%2B-6x%29%2B%2815y%2B16y%29=33%2B-2 Group like terms.


0x%2B31y=31 Combine like terms.


31y=31 Simplify.


y=%2831%29%2F%2831%29 Divide both sides by 31 to isolate y.


y=1 Reduce.


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6x%2B15y=33 Now go back to the first equation.


6x%2B15%281%29=33 Plug in y=1.


6x%2B15=33 Multiply.


6x=33-15 Subtract 15 from both sides.


6x=18 Combine like terms on the right side.


x=%2818%29%2F%286%29 Divide both sides by 6 to isolate x.


x=3 Reduce.


So the solutions are x=3 and y=1.


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 2x%2B5y=11 (red) and -3x%2B8y=-1 (green)