SOLUTION: solve the following linear equations. 4x+3y=21 9x-2y=21

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Question 458898: solve the following linear equations.
4x+3y=21
9x-2y=21
Answer by richwmiller(17219) 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:


4x%2B3y=21

9x-2y=21





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


4x%2B3y=21 Start with the given equation



3y=21-4x Subtract 4+x from both sides



3y=-4x%2B21 Rearrange the equation



y=%28-4x%2B21%29%2F%283%29 Divide both sides by 3



y=%28-4%2F3%29x%2B%2821%29%2F%283%29 Break up the fraction



y=%28-4%2F3%29x%2B7 Reduce



Now lets graph y=%28-4%2F3%29x%2B7 (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+%28-4%2F3%29x%2B7%29+ Graph of y=%28-4%2F3%29x%2B7




So let's solve for y on the second equation


9x-2y=21 Start with the given equation



-2y=21-9x Subtract 9+x from both sides



-2y=-9x%2B21 Rearrange the equation



y=%28-9x%2B21%29%2F%28-2%29 Divide both sides by -2



y=%28-9%2F-2%29x%2B%2821%29%2F%28-2%29 Break up the fraction



y=%289%2F2%29x-21%2F2 Reduce





Now lets add the graph of y=%289%2F2%29x-21%2F2 to our first plot to get:


Graph of y=%28-4%2F3%29x%2B7(red) and y=%289%2F2%29x-21%2F2(green)


From the graph, we can see that the two lines intersect at the point (3,3) (note: you might have to adjust the window to see the intersection)