What is the solution set of this system of equations?

y = x2 − 3x − 4
x = y + 8

Solutions ( 14 , 6) ( 4 , -4).

Step-by-step explanation:

Given  : y = x² − 3x − 4  and x = y + 8.

To find : What is the solution set of this system of equations.

Solution : We have given

y = x² − 3x − 4  (1)

x = y + 8 (2)

Plug the equation 2 in equation 1.

y =  (y +2)² − 3( y + 8) − 4  .

y = y² + 4 + 2y - 3y - 24 - 4 .

y = y² - y + 4 - 24 - 4.

y = y² - y - 24

On subtracting both sides by y

y² - 2y - 24 = 0.

On factoring

y² - 6y + 4y - 24 = 0.

On taking common y from first two term and 4 from last two terms.

y ( y - 6)  + 4 ( y - 6) = 0.

On grouping

(y -6) ( y + 4) = 0

For y - 6 = 0

y = 6

For y +4 = 0

y = -4.

Plug y =6 in equation 2

x = 6 + 8

x = 14.

Plug y = - 4 in equation 2.

x = -4 + 8

x = 4.

Solutions ( 14 , 6) ( 4 , -4).

Therefore, Solutions ( 14 , 6) ( 4 , -4).

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm