How many solutions does the system have?

Question

12x−15y=18
4x−5y=6

Answer 1

To determine the number of solutions for this system of equations, we can use the method of elimination:

1) Multiply both sides of the first equation by 4:
48x - 60y = 72

2) Multiply both sides of the second equation by 3:
12x - 15y = 18

At this point, we can see that if we subtract the second equation from the first equation, the y terms will be eliminated:

(48x - 60y) - (12x - 15y) = 72 - 18
48x - 60y - 12x + 15y = 54x - 45y = 54

Simplifying, we get:
54x - 45y = 54

So, this system of equations can be simplified to a single equation: 54x - 45y = 54

Since there is only one equation, the system has infinite solutions, meaning every point on this line is a solution to the system of equations.

Answer 2

Solve the system of equations.
6x–5y=27

3x+5y=36