How many solutions does the system have?

Question

x+y = 3
5x + 6y= =15

Answer 1

To find the number of solutions for the system, we can check if the two equations are dependent or independent.

First, let's rewrite the second equation in terms of x:
5x + 6y = 15
6y = 15 - 5x
y = (15 - 5x)/6

Now, we have the system of equations:
x + y = 3
y = (15 - 5x)/6

Rearranging the first equation:
x = 3 - y

Substituting this value of x into the second equation:
y = (15 - 5(3 - y))/6
y = (15 - 15 + 5y)/6
y = 5y/6

Multiplying both sides of the equation by 6:
6y = 5y

Subtracting 5y from both sides:
y = 0

Substituting this value of y back into the first equation:
x + 0 = 3
x = 3

Hence, the system has a unique solution, where x = 3 and y = 0.