Question

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x − y = −5 12x − 3y = 15 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =

Answer 1

NO SOLUTION.

Explanation:

4x - y = -5

12x - 3y = 15

Multiply the first equation by 3:

12x - 3y = -15

Note that the left side of this equation is the same as the left side of the second one, but the right sides are different. The left side cannot be equal to 2 different values. Therefore there is NO SOLUTION.

Note if we subtract the last 2 equations we get:

0 = 30 which is, of course, absurd.