How do you find five ordered pairs of 2x-3y=18?

Question

Avery Alexander · Accepted Answer

Change the equation to read either #y = .... or x = ....#

Then by choosing either an x-value or a y-value you can work out the other one. You can find infinitely many points (ordered pairs) this way.

#2x= 3y +18 rArr x = 3/2y +9" "# (Choose multiples of 2 for y)

#2x -18 = 3y rArr y = 2/3x-6 " "# (Choose multiples of 3 for x)

For example if :

#y = 8, x = 12+9 = 21 rArr (21,8)#

#x = 9, x = 6-6 = 0 rArr (9,0)#

Abigail Allen · Answer

undefined To find ordered pairs for the equation $2x - 3y = 18$, you can arbitrarily choose values for $x$ and solve for $y$, or vice versa. Here are five ordered pairs:

1. Let $x = 0$:
   $2(0) - 3y = 18$
   $-3y = 18$
   $y = -6$
   Ordered pair: (0, -6)

2. Let $y = 0$:
   $2x - 3(0) = 18$
   $2x = 18$
   $x = 9$
   Ordered pair: (9, 0)

3. Let $x = 3$:
   $2(3) - 3y = 18$
   $6 - 3y = 18$
   $-3y = 12$
   $y = -4$
   Ordered pair: (3, -4)

4. Let $y = 6$:
   $2x - 3(6) = 18$
   $2x - 18 = 18$
   $2x = 36$
   $x = 18$
   Ordered pair: (18, 6)

5. Let $x = -3$:
   $2(-3) - 3y = 18$
   $-6 - 3y = 18$
   $-3y = 24$
   $y = -8$
   Ordered pair: (-3, -8)