Question

Y= 2x+5

(3x+6y=15

Kareena says the system has one solution

Austin says the system has an infinite number of solutions

Wesley says the system has no solutions

Who do you agree with and why?

Answer 1

Kareena is correct; the system of equations has one solution. By substituting the first equation into the second and solving for x and then y, we find the unique solution (x, y) = (-1, 3).

Step-by-step explanation:

Firstly, to determine the number of solutions the system of equations has, we can compare the equations or attempt to solve them. The given system of equations is:

• y = 2x + 5
• 3x + 6y = 15

We can substitute the first equation into the second to solve for x:

• 3x + 6(2x + 5) = 15
• 3x + 12x + 30 = 15
• 15x + 30 = 15
• 15x = -15
• x = -1

Now, substitute x back into the first equation:

• y = 2(-1) + 5
• y = -2 + 5
• y = 3

Both equations can be satisfied with x=-1 and y=3, which means there is one solution to this system. Therefore, I agree with Kareena's assertion that the system has one solution because we were able to find a unique pair (x, y) that satisfies both equations.