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

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.

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

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