For what values of a and b does the following pair of linear equations have an infinite number of solutions (i) 2x+3y=9 and (a+b)x + (2a-b)y=3(a+b+1) answer

We are given

system of equations as

It will have infinite solution when both equations will become same

so, we will set coefficients of x and y of both terms equal

We can see

coefficient of x in first equation is 2

coefficient of x in second equation is a+b

so, we get

coefficient of y in first equation is 3

coefficient of y in second equation is 2a-b

so, we get

now, we can find b from first equation

we can plug it in above equation

now, we can solve for a

we get

now, we can find b

so,

.................Answer

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w