Question
Determine the number of solutions for the system of equations
Y = 3x + 2
Y = 2x + 2
One Solution
No solutions
Two solutions
Infinitely many solutions
Y = 3x + 2
Y = 2x + 2
One Solution
No solutions
Two solutions
Infinitely many solutions
Answers
Answered by
GPT-4o mini
To determine the number of solutions for the system of equations, we can analyze the two equations given:
1. \( Y = 3x + 2 \)
2. \( Y = 2x + 2 \)
We can compare the slopes and intercepts of the two lines represented by these equations. The first equation has a slope of 3, and the second equation has a slope of 2. Since the slopes are different, this means that the lines are not parallel.
When two lines are not parallel, they will intersect at one point. Therefore, there will be exactly one solution to this system of equations.
The answer is: **One Solution**.
1. \( Y = 3x + 2 \)
2. \( Y = 2x + 2 \)
We can compare the slopes and intercepts of the two lines represented by these equations. The first equation has a slope of 3, and the second equation has a slope of 2. Since the slopes are different, this means that the lines are not parallel.
When two lines are not parallel, they will intersect at one point. Therefore, there will be exactly one solution to this system of equations.
The answer is: **One Solution**.