Gre math question I don't understand. If 3c+6d=24 and 4a+3d=18, what does A equal in terms of C?

Repost, but i did it wrong before.

Gre math question I don't understand. If 3c+6d=24 and 4a+3d=18, what does A equal in terms of C?
They are asking you to cancel out the variable d from the two simultaneous equations:





3c + 6d = 24 ................ (i)


4a + 3d = 18 .................(ii)





to leave an equation is just a and c. You then rearrange to place all terms in a on the LHS and c on RHS to leave a = f(c) - i.e. a as a function of c





To handle the simulataneous equations, you can use two techniques:





1) Elimination:





Starting with:





3c + 6d = 24 ................ (i)


4a + 3d = 18 .................(ii)





Multiply (ii) by -2 and add the equations together:





3c + 6d = 24 ................ (i)


-8a - 6d = -36 .................(ii)*-2


--------------------------------------...


3c - 8a + 0d = 24 - 36 = -12





So





8a - 3c = 12





And so rearranging





a = (12 + 3c)/8





Which is the answer





Or 2) Substitution:





Take (i) and rearrange to get just d on LHS and c on RHS:





3c + 6d = 24 ................ (i)





6d = 24 - 3c


d = 4 - c/2





And then substitute that for d in equation (ii):





4a + 3d = 18 .................(ii)


4a + 3*(4-c/2) = 18


4a + 12 - 3c/2 = 18


4a - 3c/2 = 6


8a - 3c = 12


a = (12 +3c)/8





The same answer as before
Reply:We need to find out about A


A is in only one equation





4a+3d=18


(separate out the a term)


4a+3d - 3d =18 - 3d


4a =18 - 3d


(simplify the a term)


4a / 4 =( 18 - 3d ) / 4


a =( 18 - 3d ) / 4





to find out anything more about a, we need to look at d


d is in one equation





3c+6d=24


(separate out the d term)


3c+6d - 3c =24 - 3c


6d = 24 - 3c


(simplify the a term)


6d / 6 = ( 24 - 3c ) / 6


d = ( 24 - 3c ) / 6


d = 4 - 1/2c





substitute this value of d into the simplified version of the first equation





a =( 18 - 3d ) / 4 %26amp;%26amp; d = 4 - 1/2c


(locate the target)


a =( 18 - 3[d] ) / 4


(substitute)


a =( 18 - 3[ 4 - 1/2c ) ] / 4


(this should be simplified as well)





a is now in terms of c


or


the value of a is a function of the value of c
Reply:solve for a


4a+3d=18


4a=18-3d


a=18/4-3d/4





solve for d


3c+6d=24


6d=24-3c


d=4-(1/2)c





replace d with 4-(1/2)c


a=18/4-3/4(4-(1/2)c


a=18/4-12/4-3/8c


a=6/4-3/8c


a=3/2-3/8c
Reply:u have to substitute the value of a in c .
Reply:Multiply the second equation by 2.





8a+6d=36


3c+6d=24





Subtract the second from the first. Doesn't matter which is subtracted from which.





8a-3c=12


a=(12+3c)/8
Reply:First, you should notice that both equations contain a common variable, d. You must use this to your advantage. Solve the first equation for d in terms of c to get...





d = 4 - 1/2c





Next, solve the second equation for a in terms of d...





a = 18/4 - 3/4d.





Finally plug the value of d in terms of c into the equation for a and simplify...





a = 18/4 - 3/4(4 - 1/2c)


a = 18/4 - 3 + 3/8c





a = 3/2 + 3/8c
Reply:If 3c+6d=24 and 4a+3d=18, what does A equal in terms of C?


Multiply 2nd equation by -2 getting -8a -6d = -36


Add this result to 1st equation getting 3c -8a = -12


8a = 3c+12


a = (3c + 12)/8
Reply:6d = -3c + 24


d = -1/2c +4





4a+3(-1/2c+4) = 18





4a - 3/2c + 12 = 18


a = 3/2 + 3/8c