Larry C. answered • 11/15/18

Computer Science and Mathematics professional

2x + 3y = 12 is the equation of a line in standard form and, since there are an infinite number of points on a line, there are an infinite number of correct solutions.

If you have a second linear equation, then you have 3 possibilities:

- The second equation is merely a mathematical permutation of the first such as 4x + 6y = 24 and describes the same line, thus again having an infinite number of solutions.
- The second equation intersects the first in only one point and the solution is the point of intersection. For example, if the 2nd equation was x = 3: 2*3 + 3y = 12 -> 6 + 3y = 12 -> 3y = 6 -> y = 2. Therefore, the solution of that system of equations is (3, 2).
- The second equation is parallel to the first such as x + 3y = 6. In this case, the two lines never meet and there is no solution.

John R.

03/28/19