Solve the system of linear equations by substitution. x=2y+7 3x−2y=3

The system of equation
First equation
x = 2y + 7
Second equation
3x - 2y = 3

Substitute x with (2y + 7) in the second equation
3x - 2y = 3
3(2y + 7) - 2y = 3

use distributive property
3(2y) + 3(7) - 2y = 3
6y + 21 - 2y = 3

add like terms
6y - 2y + 21 = 3
4y = 3 - 21
4y = -18
  y = -18/4
  y = -4.5

Substitute y with its value, which is -4.5, in the first equation
x = 2y + 7
x = 2(-4.5) + 7
x = -9 + 7
x = -2

The solution is
(x,y) = (-2, -4.5)

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.