SOLUTION: I need help with 2 homework problems. I can use any method (elimination, subtitution or graphical methods) the problems are 5x + 6y = 14

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Question 145021: I need help with 2 homework problems. I can use any method (elimination, subtitution or graphical methods) the problems are 5x + 6y = 14
-3y + x = 7 I got (35/12, -7/12)

next problem 2x/3 + 3y/4 = 11/12

x/3 + 7y/18 = 1/2



(I got (8/5, -3/35)
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1





Start with the given system of equations:

system%285x%2B6y=14%2Cx-3y=7%29




1%285x%2B6y%29=1%2814%29 Multiply the top equation (both sides) by 1
-5%28x-3y%29=-5%287%29 Multiply the bottom equation (both sides) by -5




Distribute and multiply

5x%2B6y=14
-5x%2B15y=-35


Now add the equations together. In order to add 2 equations, group like terms and combine them

%285x-5x%29%2B%286y%2B15y%29=14-35

Combine like terms and simplify



cross%285x-5x%29%2B21y=-21 Notice how the x terms cancel out




21y=-21 Simplify




y=-21%2F21 Divide both sides by 21 to isolate y




y=-1 Reduce



Now plug this answer into the top equation 5x%2B6y=14 to solve for x

5x%2B6y=14 Start with the first equation



5x%2B6%28-1%29=14 Plug in y=-1




5x-6=14 Multiply



5x=14%2B6Add 6 to both sides


5x=20 Combine like terms on the right side


x=%2820%29%2F%285%29 Divide both sides by 5 to isolate x



x=4 Divide




So our answer is
x=4 and y=-1



which also looks like




Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of 5x%2B6y=14 (red) and x-3y=7 (green) and the intersection of the lines (blue circle).












# 2




Let's look at the first equation 2x%2F3%2B3y%2F4=11%2F12


12%282x%2Fcross%283%29%2B3y%2Fcross%284%29%29=12%2811%2Fcross%2812%29%29 Multiply both sides of the first equation by the LCD 12


8x%2B9y=11 Distribute


---------


Let's look at the second equation x%2F3%2B7y%2F18=1%2F2

18%28x%2Fcross%283%29%2B7y%2Fcross%2818%29%29=18%281%2Fcross%282%29%29 Multiply both sides of the second equation by the LCD 18


6x%2B7y=9 Distribute


---------



So our new system of equations is:


system%288x%2B9y=11%2C6x%2B7y=9%29




3%288x%2B9y%29=3%2811%29 Multiply the top equation (both sides) by 3
-4%286x%2B7y%29=-4%289%29 Multiply the bottom equation (both sides) by -4




Distribute and multiply

24x%2B27y=33
-24x-28y=-36


Now add the equations together. In order to add 2 equations, group like terms and combine them

%2824x-24x%29%2B%2827y-28y%29=33-36

Combine like terms and simplify



cross%2824x-24x%29-y=-3 Notice how the x terms cancel out




-y=-3 Simplify




y=-3%2F-1 Divide both sides by -1 to isolate y




y=3 Reduce



Now plug this answer into the top equation 8x%2B9y=11 to solve for x

8x%2B9y=11 Start with the first equation



8x%2B9%283%29=11 Plug in y=3




8x%2B27=11 Multiply



8x=11-27Subtract 27 from both sides


8x=-16 Combine like terms on the right side


x=%28-16%29%2F%288%29 Divide both sides by 8 to isolate x



x=-2 Divide




So our answer is
x=-2 and y=3



which also looks like


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
5x + 6y = 14
-3y + x = 7
------------
5x + 6y = 14
x - 3y = 7
------------
5x + 6y = 14
2x - 6y = 14
Add the 2 eqns
7x + 0y = 28
x = 4
y = -1
2nd set
2x/3 + 3y/4 = 11/12
x/3 + 7y/18 = 1/2
-----------------
Mult eqn 1 by 12, eqn 2 by 18 to eliminate fractions
8x + 9y = 11
6x + 7y = 9
------------ Mult eqn 1 by 3 and eqn 2 by 4 to get 24x in order to eliminate
24x + 27y = 33
24x + 28y = 36
Subtract 2 from 1
0x -y = -3
y = 3
Sub, and get x = -2