Question

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.
4x − y = −3
12x − 3y = 9
a. one and only one solution
b. infinitely many solutions
c. 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

multiplying the 1st eqn by 3 gives ... 12x − 3y = -9

this is the 2nd eqn , with a different constant term

this means the lines are parallel
... they never cross, so there is no solution

Answer 2

no soultion