Solve the simultaneous equations using both elimination and substitution method.

x=1 and y = 9

Step-by-step explanation:

Solving using elimination method:

In elimination method we solve equations such that one variable cancels out and we find the value of other variable.

x + 7y = 64

x + 3y = 28

Subtracting both equations:

x + 7y = 64

x + 3y = 28

-   -       -

0 +4y = 36

y= 36/4

y=9

Putting value of y in one of the equation,

x+7y = 64

x + 7(9) = 64

x + 63 = 64

x = 64-63

x = 1

So, x=1 and y=9

Solving using substitution method:

In substitution method, we substitute value of one variable into other value

x + 7y = 64   (1)

x + 3y = 28   (2)

From 1

x = 64 -7y

Putting value of x in eq(2)

(64 -7y) + 3y = 28

64 -7y +3y =28

64 - 4y = 28

-4y = 28 -64

-4y = -36

y = -36/-4

y = 9

Putting value of y in eq (1)

x + 7y = 64

x + 7(9) = 64

x + 63 = 64

x = 64 - 63

x = 1

So, x=1 and y = 9.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.