Solve the system by substitution. Show all of your work.
3x – 2y = -2
3x + y = 10

x = 2 ; y= 4

Step-by-step explanation:

3x -2y = -2

y = -3x+10

3x + 6x -20 = -2

9x = 18

x = 2

y = -6 + 10

y = 4

x = 2

y = 4

Steps:

given:

3x – 2y = -2

3x + y = 10

2y = 3x+2

y = (3x+2)/2

3x + y = 10

3x + (3x+2)/2 = 10

(6x+3x+2)/2 = 10

(9x + 2)/2 = 10

9x + 2 = 20

9x = 18

x = 2

y = 4

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.