SOLUTION: if a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. Please shopw all work. 3x+4y=5 2x

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Question 466779: if a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. Please shopw all work.
3x+4y=5
2x+y=1

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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



Start with the given system of equations:


3x%2B4y=5

2x%2By=1





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%2B4y=5 Start with the given equation



4y=5-3x Subtract 3+x from both sides



4y=-3x%2B5 Rearrange the equation



y=%28-3x%2B5%29%2F%284%29 Divide both sides by 4



y=%28-3%2F4%29x%2B%285%29%2F%284%29 Break up the fraction



y=%28-3%2F4%29x%2B5%2F4 Reduce



Now lets graph y=%28-3%2F4%29x%2B5%2F4 (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+%28-3%2F4%29x%2B5%2F4%29+ Graph of y=%28-3%2F4%29x%2B5%2F4




So let's solve for y on the second equation


2x%2By=1 Start with the given equation



1y=1-2x Subtract 2+x from both sides



1y=-2x%2B1 Rearrange the equation



y=%28-2x%2B1%29%2F%281%29 Divide both sides by 1



y=%28-2%2F1%29x%2B%281%29%2F%281%29 Break up the fraction



y=-2x%2B1 Reduce





Now lets add the graph of y=-2x%2B1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-3%2F4%29x%2B5%2F4%2C-2x%2B1%29+ Graph of y=%28-3%2F4%29x%2B5%2F4(red) and y=-2x%2B1(green)


From the graph, we can see that the two lines intersect at the point (-1%2F5,7%2F5) (note: you might have to adjust the window to see the intersection)