When the lines are parallel then there is no solution to the system of equations. This happens because the intersection is the solution. And when there is no intersection then there is no solution.
Given the system of equations y = 3/2 x − 6, y = −9/2 x + 21, since both expressions are functions of y, we will equate both of them to find the variable x;
3/2 x − 6 = −9/2 x + 21,
Cross multiplying;
3(2x+21) = -9(2x-6)
6x+63 = -18x+54
collecting the like terms;
6x+18x = 54-63
24x = -9
x = -9/24
x = -3/8
To get the value of y, we will substitute x = -3/8 into any of the given equation. Using the first equation;
