SOLUTION: solve the following system by the addition method: {7x-6y=13} by {6x-5y=11)

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Question 202430This question is from textbook introductory and intermediate algebra
: solve the following system by the addition method:
{7x-6y=13} by
{6x-5y=11) This question is from textbook introductory and intermediate algebra

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%287x-6y=13%2C6x-5y=11%29


5%287x-6y%29=5%2813%29 Multiply the both sides of the first equation by 5.


35x-30y=65 Distribute and multiply.


-6%286x-5y%29=-6%2811%29 Multiply the both sides of the second equation by -6.


-36x%2B30y=-66 Distribute and multiply.


So we have the new system of equations:
system%2835x-30y=65%2C-36x%2B30y=-66%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:


%2835x-30y%29%2B%28-36x%2B30y%29=%2865%29%2B%28-66%29


%2835x%2B-36x%29%2B%28-30y%2B30y%29=65%2B-66 Group like terms.


-x%2B0y=-1 Combine like terms.


-x=-1 Simplify.


x=%28-1%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=1 Reduce.


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35x-30y=65 Now go back to the first equation.


35%281%29-30y=65 Plug in x=1.


35-30y=65 Multiply.


-30y=65-35 Subtract 35 from both sides.


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


y=%2830%29%2F%28-30%29 Divide both sides by -30 to isolate y.


y=-1 Reduce.


So the solutions are x=1 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 7x-6y=13 (red) and 6x-5y=11 (green)