SOLUTION: The equations of two lines are given as 3w-2z=42 and 2w -z = 26. What are the coordinates of the point of intersection? Thanks for the help!

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Question 176933: The equations of two lines are given as 3w-2z=42 and 2w -z = 26. What are the coordinates of the point of intersection?

Thanks for the help!
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%283w-2z=42%2C2w-z=26%29


-2%282w-z%29=-2%2826%29 Multiply the both sides of the second equation by -2.


-4w%2B2z=-52 Distribute and multiply.


So we have the new system of equations:
system%283w-2z=42%2C-4w%2B2z=-52%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:


%283w-2z%29%2B%28-4w%2B2z%29=%2842%29%2B%28-52%29


%283w%2B-4w%29%2B%28-2z%2B2z%29=42%2B-52 Group like terms.


-w%2B0z=-10 Combine like terms.


-w=-10 Simplify.


w=%28-10%29%2F%28-1%29 Divide both sides by -1 to isolate w.


w=10 Reduce.


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3w-2z=42 Now go back to the first equation.


3%2810%29-2z=42 Plug in w=10.


30-2z=42 Multiply.


-2z=42-30 Subtract 30 from both sides.


-2z=12 Combine like terms on the right side.


z=%2812%29%2F%28-2%29 Divide both sides by -2 to isolate z.


z=-6 Reduce.


So our answer is w=10 and z=-6.


So the point of intersection is .


This means that the system is consistent and independent.