Find two numbers such that the smaller subtracted from the larger is 9 and the difference of the square of the larger subtracted from square of the smaller is 9

GIVEN - The subtraction of the smaller number from the larger number be 9.

The subtraction of the square of the smaller number from the square larger number be 9.

Find the number

to proof =

let larger number be x

and let  the smaller number be y

and the second equation becomes

by using the equation

we have

= (x - y) (x +y)

now put this in the above equation we get

thus we  have

(x-y) (x+y) = 9

as we have (x-y) =9

put in the above equation

we get

(x + y ) =1

by solving the equation (x + y ) = 1 &  (x - y) = 9

we get x = 5 & y = -4

Hence proved

the answer is c)8

step-by-step explanaction:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is