SOLUTION: Solve each system by graphing. Write no solution or infinitely many solutions where appropriate. Make sure to show your graph and also show your check verifying that your answer

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Question 945191: Solve each system by graphing. Write no solution or infinitely many solutions where appropriate. Make sure to show your graph and also show your check verifying that your answer is correct.
Y = x
2x + y = 3/2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+x .........write in standard form
2x+%2B+y+=+3%2F2....both sides multiply by 2
---------------
-x%2By+=+0
4x+%2B+2y+=+3

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



Start with the given system of equations:


-x%2By=0

4x%2B2y=3





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


-x%2By=0 Start with the given equation



1y=0%2Bx Add +x to both sides



1y=%2Bx%2B0 Rearrange the equation



y=%28%2Bx%2B0%29%2F%281%29 Divide both sides by 1



y=%28%2B1%2F1%29x%2B%280%29%2F%281%29 Break up the fraction



y=x%2B0 Reduce



Now lets graph y=x%2B0 (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+x%2B0%29+ Graph of y=x%2B0




So let's solve for y on the second equation


4x%2B2y=3 Start with the given equation



2y=3-4x Subtract 4+x from both sides



2y=-4x%2B3 Rearrange the equation



y=%28-4x%2B3%29%2F%282%29 Divide both sides by 2



y=%28-4%2F2%29x%2B%283%29%2F%282%29 Break up the fraction



y=-2x%2B3%2F2 Reduce





Now lets add the graph of y=-2x%2B3%2F2 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B0%2C-2x%2B3%2F2%29+ Graph of y=x%2B0(red) and y=-2x%2B3%2F2(green)


From the graph, we can see that the two lines intersect at the point (1%2F2,1%2F2) (note: you might have to adjust the window to see the intersection)