How do you know how to add or subtract a simultaneous equation? Here is a couple of example's ...?

Question

Thanks for all your help on simultaneous equation's. Though I am still stuck on how do you know weather to add or subtract a simultaneous equation. Here is a couple of example's. 5x + 7y = 12 3x + 7y = 10 and 33x + 23y = 56 35x -23y =13. There is no need to solve these equation's if you could just give me a good explanation of how I would know weather to add or subtract them.

Answer 1

if the coefficients and the signs arethe same subtract
if the coefficients are the same but the signs are different then add
5x+7y=12
3x+7y=10
subtract
2x=2 x=1 substitute to get y

33x+23y=56
35x-23y=13
adding
68x=69
now x=69/68 (check your sum)
substiute to get y

Answer 2

You add where adding gets rid of one variable and subtract where subtraction gets rid of one variable.

In example 1 you subtract since this gets rid of the y variable.

giving 2x equals 2 or x equals= 1.
resubstituting the x value of 1 in either equation gives y = 1

note if you added you would get 8x + 14y = 22 offering no solution

In example 2 you add since this gets rid of the y factor . Unfortunately the answer is x = 69/68 providing a many decimal result ofr y when substituted.

I imagine the problem should have read 33x + 23 y = 55 [not 56]to make the answer easier, with x = 1 again.but the equations as given provide the more difficult number

To solve the problem you must reduce the equation to one variable so you add if that gets rid of one variable and you subtract if that gets rid of one variable.

Answer 3

The point of simultaneous equations is to eliminate ONE of the variables. This usually means adding or subtracting them, but it does not have to. In your case, it looks easier if you eliminate d. To do this multiply the top equation by 3 and the bottom one by 2 and add. This will get rid of d and leave an equation in c only. However, if you wanted to eliminate c, you would multiply the top by 4, the bottom by 6 and subtract, leaving you with an equation in d only. You can tell whether to add or subtract by looking at the signs of c and d in the equations. That is all there is to it.

Answer 4

Remember that the goal is to get one of the variables to "disappear" -- i.e., cancel out. In order for this to happen, either

1. the coefficients of that variable need to be equal, in which case you'd subtract the equations, or
2. the coefficients of that variable need to be equal in magnitude, but opposite in sign -- in which case, you add the equations.

Your first case is an example of #1, and your second case is an example of #2.

What might help, though, is if you make it your goal to make the coefficients of your "target variable" opposite in sign. Then you can consistently add the equations. In your case #1, you could multiply both sides of Eq 2 by -1, making it -3x - 7y = -10. Then you can just add the two equations together, and the 7y and -7y will cancel each other out.

Hope that helps!

Answer 5

I want to say that for the simple equations you have given, the adding subtracting strategy works. It is probably fine for your level of math. However, it only works in those simple cases. The general way to solve a syste of euqations is to solve one equation for X or Y and then pluggin in thtat solution into the other equation.

5x + 7y = 12, 3x + 7y = 10

for example you can solve for Y as y= (12-5x)/7 and then plug that in for Y in the second equation. then solve for X.

Answer 6

5x + 7y = 12
3x + 7y = 10
---------------- subtract
2x + 0y = 2

which simplifies to 2x = 2. This helps you solve the equation.

33x + 23y = 56
35x - 23y = 13
-------------------- add
68x + 0y = 69

so 68x = 69

Add or subtract, whatever is needed to get a zero coefficient for x or y.

Answer 7

You add them if one variable is the opposite of the one directly below it; you subtract them of one variable is the same as the one directly below. So subtract in (1) becayse 7y is over 7y, and add in (2) because 23y is over -23y.

Answer 8

the Basic idea is to eliminate one variable from the equation. If coefficients of x (or y) are of same sign - you subtract, If different sign - add.

Answer 9

Take the first two eqns. Do you observe 7y in both? You subtract to cancel out this term. So you can work out x
Our aim is to cancel out one variable. you see the next eqn. in one eqn you have +23y in the other you have -23y. So what should you do to cancel this term? you add! then solve for x .Got it?

Answer 10

you add like term like 7y and 7y