Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x − y = 2 3x + y = −6 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:Only one solution(x, y) = (-0.8, -3.6)Step-by-step explanation:You know there is only one solution because the ratio of x- and y-coefficients is different in the two equations. That means the lines will have different slopes, so must intersect in exactly one point.__The y-coefficients are opposites, so you can eliminate the y-variable by adding the equations:   (2x -y) + (3x +y) = (2) + (-6)   5x = -4   x = -4/5 = -0.8Substituting this into the second equation, we have ...   3(-0.8) +y = -6   y = -3.6 . . . . . . . add 2.4 to both sidesThe solution is (x, y) = (-0.8, -3.6).__You can also find the solution by graphing (or using a graphing calculator).