Question

Which statement is true about the equations –3x + 4y = 12 and x – y = 1? The system of the equations has exactly one solution at (–8, 3). The system of the equations has exactly one solution at (–4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.

Answer 1

The equations are:
                        -3x + 4y = 12
                           x - y = 1

We solve for the solution by the substitution method. From the second equation,
                          x = 1 + y

We substitute x of the first equation with the expression derived above.
 
                       -3(1 + y) + 4y = 12
                           -3 -3y + 4y = 12
                               y - 3 = 12
Transposing,
                                   y = 15
Substituting this to the expression for x,
                       x = 1 + y = 1 + 15 = 16

Thus, the solution is (16,15). 

Thus, the equations has exactly one solution which is equal to (16,15).