SOLUTION: Solve the system of equations; If you cannot find a solution, label the lines as parallel or coinciding and explain why. 3x-y=2 16x-5y=11

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the system of equations; If you cannot find a solution, label the lines as parallel or coinciding and explain why. 3x-y=2 16x-5y=11      Log On


   

Question 455015: Solve the system of equations;
If you cannot find a solution, label the lines as parallel or coinciding and explain why.
3x-y=2
16x-5y=11
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3x-y=2
16x-5y=11

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x-y=2

16x-5y=11





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


3x-y=2 Start with the given equation



-y=2-3x Subtract 3+x from both sides



-y=-3x%2B2 Rearrange the equation



y=%28-3x%2B2%29%2F%28-1%29 Divide both sides by -1



y=%28-3%2F-1%29x%2B%282%29%2F%28-1%29 Break up the fraction



y=3x-2 Reduce



Now lets graph y=3x-2 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-2%29+ Graph of y=3x-2




So let's solve for y on the second equation


16x-5y=11 Start with the given equation



-5y=11-16x Subtract 16+x from both sides



-5y=-16x%2B11 Rearrange the equation



y=%28-16x%2B11%29%2F%28-5%29 Divide both sides by -5



y=%28-16%2F-5%29x%2B%2811%29%2F%28-5%29 Break up the fraction



y=%2816%2F5%29x-11%2F5 Reduce





Now lets add the graph of y=%2816%2F5%29x-11%2F5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-2%2C%2816%2F5%29x-11%2F5%29+ Graph of y=3x-2(red) and y=%2816%2F5%29x-11%2F5(green)


From the graph, we can see that the two lines intersect at the point (1,1) (note: you might have to adjust the window to see the intersection)