Find the length of qs if q is the midpoint of ps, pg

Comment

Q is the midpoint  means that the two line segments are equal.

Equation

5x + 1 = 3x + 16

Solve

Subtract 1 from both sides.

5x = 3x + 16 - 1

5x = 3x + 15              Subtract 3x from both sides.

5x - 3x = 15        

2x = 15                      Divide by 2

x = 15/2

x = 7.5

Check

3(7.5) + 16 =? 5(7.5) + 1

22.5 + 16 =? 37.5 + 1

38.5 =? 38.5 and they do check.

i used to know how to do this in 7th but i forget easily

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1