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)   (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:










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


Start with the given equation



Subtract from both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce



Now lets graph (note: if you need help with graphing, check out this solver)



Graph of




So let's solve for y on the second equation


Start with the given equation



Subtract from both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce





Now lets add the graph of to our first plot to get:


Graph of (red) and (green)


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