SOLUTION: Solve the following system of equations. Enter the x-coordinate of the solution Round your answer to the nearest tenth. 5x+2y=22 -2x+6y=3

Algebra ->  Linear-equations -> SOLUTION: Solve the following system of equations. Enter the x-coordinate of the solution Round your answer to the nearest tenth. 5x+2y=22 -2x+6y=3      Log On


   

Question 980125: Solve the following system of equations. Enter the x-coordinate of the solution Round your answer to the nearest tenth. 5x+2y=22 -2x+6y=3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

5x%2B2y=22
+-2x%2B6y=3
-------------------
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


5x%2B2y=22

-2x%2B6y=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


5x%2B2y=22 Start with the given equation



2y=22-5x Subtract 5+x from both sides



2y=-5x%2B22 Rearrange the equation



y=%28-5x%2B22%29%2F%282%29 Divide both sides by 2



y=%28-5%2F2%29x%2B%2822%29%2F%282%29 Break up the fraction



y=%28-5%2F2%29x%2B11 Reduce



Now lets graph y=%28-5%2F2%29x%2B11 (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+%28-5%2F2%29x%2B11%29+ Graph of y=%28-5%2F2%29x%2B11




So let's solve for y on the second equation


-2x%2B6y=3 Start with the given equation



6y=3%2B2x Add 2+x to both sides



6y=%2B2x%2B3 Rearrange the equation



y=%28%2B2x%2B3%29%2F%286%29 Divide both sides by 6



y=%28%2B2%2F6%29x%2B%283%29%2F%286%29 Break up the fraction



y=%281%2F3%29x%2B1%2F2 Reduce





Now lets add the graph of y=%281%2F3%29x%2B1%2F2 to our first plot to get:


Graph of y=%28-5%2F2%29x%2B11(red) and y=%281%2F3%29x%2B1%2F2(green)


From the graph, we can see that the two lines intersect at the point (63%2F17,59%2F34) (note: you might have to adjust the window to see the intersection)



your answer to the nearest tenth:
the point (3.7,1.7)