Question

x is bigger than y . The difference between x and y is 18 . Find x and y .
Please answer this question .

Answer 1

Answer:

If x and y are positive, which of the following must be greater than ?

1.

2.

3.

(A) None

(B) 1 only

(C) 2 only

(D) 1 and 3 only

(E) 2 and 3 only

First of all is always positive. This by the way eliminates option III right away as (numereator) may or may not be positive, so we should concentrate on I and II

Next:

is always great than (well in fact if both and are 0, they are equal but it's not the case as given that and are positive). To check this: square them

Let's proceed:

SOLUTION #1

I. --> nominators are the same, obviously denominator may or may not be greater than . OUT.

II. --> denominators are the same and nominator (as we've already discussed above) is always greater than . OK

III. Well we can not even consider this one as our expression is always positive and the (numerator) can be negative. OUT

Answer C. Another way of solving a linear system is to use the elimination method. In the elimination method you either add or subtract the equations to get an equation in one variable.

When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Example

3y+2x=65y−2x=10

We can eliminate the x-variable by addition of the two equations.

3y+2x=6

+5y−2x=10−−−−−−−−−−−−

=8y=16

y=2

The value of y can now be substituted into either of the original equations to find the value of x

3y+2x=6

3⋅2+2x=6

6+2x=6

x=0

The solution of the linear system is (0, 2).

To avoid errors make sure that all like terms and equal signs are in the same columns before beginning the elimination. you must follow this method