Consider the following system of equations. x+y=11 and 2x - 3y=-3. which equation can be added to the system so that the solution does not change.

a) x-y=2
b) -2x+2y=-2
c)3x+y=20
d)x+2y=18

B) -2x+2y=-2

Step-by-step explanation:

we have

----> equation A

----> equation B

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (6,5)

see the attached figure

Remember that

If a equation is added to the system so that the solution does not change, then the solution of the system must be a solution of the equation added

Verify each case

The solution of the system is (6,5)

substitute the value of x and the value of y in each equation

case A) x-y=2

6-5=2

1=2 ----> is not true

therefore

This equation can't be added to the system

case B) -2x+2y=-2

-2(6)+2(5)=-2

-12+10=-2

-2=-2 ----> is true

therefore

This equation can be added to the system

case C) 3x+y=20

3(6)+5=20

18+5=20

23=20 ----> is not true

therefore

This equation can't be added to the system

case D) x+2y=18

5+2(6)=18

5+12=18

17=18 ----> is not true

therefore

This equation can't be added to the system

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

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step-by-step explanation: