SOLUTION: the elimination method show work if the system has no solution or an infinite number of solutions state this 3x - 2y = 11 6x + 11y = 97

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Question 590780: the elimination method show work if the system has no solution or an infinite number of solutions state this
3x - 2y = 11
6x + 11y = 97
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-2y=11%2C6x%2B11y=97%29


-2%283x-2y%29=-2%2811%29 Multiply the both sides of the first equation by -2.


-6x%2B4y=-22 Distribute and multiply.


So we have the new system of equations:
system%28-6x%2B4y=-22%2C6x%2B11y=97%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:


%28-6x%2B4y%29%2B%286x%2B11y%29=%28-22%29%2B%2897%29


%28-6x%2B6x%29%2B%284y%2B11y%29=-22%2B97 Group like terms.


0x%2B15y=75 Combine like terms.


15y=75 Simplify.


y=%2875%29%2F%2815%29 Divide both sides by 15 to isolate y.


y=5 Reduce.


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-6x%2B4y=-22 Now go back to the first equation.


-6x%2B4%285%29=-22 Plug in y=5.


-6x%2B20=-22 Multiply.


-6x=-22-20 Subtract 20 from both sides.


-6x=-42 Combine like terms on the right side.


x=%28-42%29%2F%28-6%29 Divide both sides by -6 to isolate x.


x=7 Reduce.


So the solutions are x=7 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-2y=11 (red) and 6x%2B11y=97 (green)

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