If B is the midpoint of AC, AB = 6x + 1 and BC = 3x + 10, then what is the length of AC?

AC = 38

Step-by-step explanation:

A mid point divides a line in 2 equal parts. That means that one segment is equal to the other.

6x + 1 = 3x + 10                 Subtract 3x from both sides

6x-3x + 1 = 3x -3x + 10     Combine

3x + 1 = 10                         Subtract 1 from both sides

3x + 1 -1 = 10 - 1

3x = 9                                Divide by 3

3x/3 = 9/3

x = 3

6x + 1 = 6*3 + 1 = 19

3x +10= 3*3 + 10 = 19

Both segments are 19 units long

AC = 19 + 19 = 38

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.