(5,1) is a solution to the equation 2x - 3y = 7. What does this mean?

Question

(5,1) is a solution to the equation 2x - 3y = 7.  What does this mean?

anonymous · Answer

Think of the line graph of that equation.  It is really just all the individual points that make it true (the left equals the right).  So the x,y coordinates x=2 and y= -1 can be substituted for their variables on the left side of the equation and the equation will simplify down to 7 = 7 , which is true.  So the point (2,-1) will be found on the line graph of that equation.
Substituting 5 for x and 1 for y also makes the equation 7=7 after simplifying so the point (5,) is a solution and also happens to be on the line for the function: 2x-3y=7.
Note:  x=4 and y=1 give 8-3=7 which is NOT true so (4,1) is said NOT to satisfy the equation and is NOT a solution for the function 2x - 3y = 7.

anonymous · Answer

[ ... and (4,1) is NOT found on the graph of 2x-3y=7. ]