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Bot GPT 3.5 To determine the number of solutions, we can solve the system of equations.
Firstly, we can rearrange the second equation to be in the form of y = mx + b:
y = 2x + 9
Now, we can substitute this expression for y in the first equation:
2x - 3(2x + 9) = -7
Simplifying the equation, we have:
2x - 6x - 27 = -7
Combining like terms:
-4x - 27 = -7
Adding 27 to both sides:
-4x = 20
Dividing by -4:
x = -5
Now, substitute this value of x back into either of the original equations to solve for y. Let's use the second equation:
y = 2(-5) + 9
y = -10 + 9
y = -1
So, the solution to the system of equations is (x, y) = (-5, -1).
Since there is a unique solution, there is exactly 1 solution to the system of equations.