Question

Consider the equation y = 15x - 45, and y = 12x + 18. How many solutions does the equation have? Solve the equation 15x - 45 = 12x + 18 to confirm your answer regarding the number of solutions.

a) One solution
b) No solution
c) Infinite solutions
d) Two solutions

Answer 1

The equation has one solution.

Step-by-step explanation:

The given equations are y = 15x - 45 and y = 12x + 18. To determine the number of solutions, we can compare the slopes of the equations. The slopes of the equations are 15 and 12, which are different. Therefore, the equations intersect at a single point and have one solution.

To confirm the answer, we can solve the equation 15x - 45 = 12x + 18. By subtracting 12x from both sides, we get 3x - 45 = 18. Next, adding 45 to both sides gives 3x = 63. Finally, dividing both sides by 3 gives x = 21. Since x has a unique value, the equation has one solution.