SOLUTION: I usually know how to do questions involving substitution but this one is really proving difficult x/3+y/2=-4 x-3y=6 I tried substituting for the x but I'm not even sure

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: I usually know how to do questions involving substitution but this one is really proving difficult x/3+y/2=-4 x-3y=6 I tried substituting for the x but I'm not even sure      Log On


   

Question 1000186: I usually know how to do questions involving substitution but this one is really proving difficult
x/3+y/2=-4
x-3y=6
I tried substituting for the x but I'm not even sure where to go from there
Found 3 solutions by josgarithmetic, addingup, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!

First Equation
x%2F3%2By%2F2=-4
y%2F2=-x%2F3-4
y=-%282%2F3%29x-12

Second Equation
x-3y=6
-3y=-x%2B6
y=x%2F3-2

The system should be solvable.
Both formulas for y can be shown equated to find a solution.
highlight_green%28-%282%2F3%29x-12=x%2F3-2%29----equating the two y expressions
-%282%2F3%29x-12-%281%2F3%29x=-2
-x-12=-2
x%2B12=-2
highlight%28x=-14%29

Using the y equivalent of the second equation:
y=x%2F3-2
y=14%2F3-2
y=14%2F3-6%2F3
highlight%28y=8%2F3%29

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
x/3+y/2=-4
x-3y=6
--------------------
Let's begin by getting the fractions out of the way. On the first equation, multiply both sides by 6 (because 6 is a common denominator for 3 and 2):
x/3+y/2=-4
6(x/3)+6(y/2)= 6(-4)
2x+3y= -24 This is now our 1st equation.
-----------------------------
x-3y= 6 Add 3y on both sides:
x= 6+3y Now let's substitute this value for x:
-------------------------------
2(6+3y)+3y= -24
12+6y+3y= -24 Subtract 12 from both sides and add y on left
9y= -36 Divide by 9
y= -4
And we said that x was:
x= 6+3y
x= 6+3(-4)
x= 6+-12
x= - 6
------------------
Proof:
x/3+y/2=-4
-6/3+-4/2= -4
-2+-2= -4 We have the correct answer here. You do the same with the other equation and you'll find we have the correct answer.
---------------------------------------
Now let’s find x:
x= 6+3(-4)
x= 6- 12
x= -6

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!

I usually know how to do questions involving substitution but this one is really proving difficult
x/3+y/2=-4
x-3y=6
I tried substituting for the x but I'm not even sure where to go from there 
x%2F3+%2B+y%2F2+=+-+4

2x + 3y = - 24 -------- Multiplying by LCD, 6 ------- eq (i)

 x - 3y =    6 -------- eq (ii)

3x      = - 18

x+=+%28-+18%29%2F3, or highlight_green%28x+=+-+6%29

Now all you have to do is substitute - 6 for x in any of the 2 original equations to determine the value of y



You can solve eq (ii) for x to get: x = 6 + 3y, but after multiplying the 1st equation by 6, it's obvious

that y can immediately be eliminated to get the value of x