The system of equations above has how many solutuions?

2b = 8a

Step-by-step explanation:

The main thing you have to remember before answering the question is

if :

The system has 1 and only solution, then the system will be a1/a2 not equal to b1/b2 =c1/c2

The system has infinitely many solutions then the system will be a1/a2=b1/b2 =c1/c2

The system has no solutions then it will be a1/a2 = b1/b2 not equal to c1/c2

Here, ax +by =12; 2x + 8y =60

The system is required to have infinite no. of solutions.

Therefore,

a1/a2=b1/b2=c1/c2

a1/a2= a/2 (coefficients of x)

b1/b2= b/8 (coefficients of y)

c1/c2 = -12/60= 1/5 ( constant terms)

Therefore,

a/2 =b/8 = 1/5

Since a/2 =b/8 then,

2b = 8a

Here, we have to find a/b by transposing.

It is better to take all the variables to one side,

b/a = 8/2 =4

So a/b will be directly the reverse of it.

Therefore if b/a =4

Then a/b = 1/4

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet