Answer:
the solutions are all the ordered pairs (x, (2/3)x + 2), where x is any real number.
Step-by-step explanation:
-2x + 3y = 6 -6x + 9y = 18
We can see that the second equation is just three times the first. If we simplify the second equation by dividing it by 3, we get:
-2x + 3y = 6 -2x + 3y = 6
This means that both equations represent the same line, so they are dependent and have an infinite number of solutions. The solution to this system is not a single ordered pair but all the points on the line given by the equation -2x + 3y = 6.
To find the solutions in terms of ordered pairs, we can solve for y in terms of x using the first equation:
3y = 2x + 6 y = (2/3)x + 2
So, the solutions are all the ordered pairs (x, (2/3)x + 2), where x is any real number.
