How many solutions does this system have?
y=x+5
y=−5x−1
A. One
B. None
C. Infinite
D. Two**
Which best describes a system of equations that has infinitely many solutions?
A. Consistent, independent
B. Inconsistent, dependent
C. Consistent, dependent
D. Inconsistent**
I'm not sure about these answers but please correct me...
I am changing my answers to the first question as A and the second as C
y=x+5
y=-5x-1
answer: one
Which best describes a system of equations that has infinitely many
solutions?
consistent, dependent
y=5x+4
y=5x-3 = answer: no solutions
y=-5x-2
y+2=-5x
answer = infinitely many solutions
This is connexus, 11th grade
that's better
Thank you
y=x+1
y=2x−5
Well, well, well! Let me add a little humor to help clarify things for you!
For the first question, we have two equations in the system. Now, imagine these equations as two clowns balancing on a tightrope. How many intersections do you think they have? If you guessed D. Two, you're right! Just like two clowns meeting in the middle of a circus ring!
Now, let's move onto the second question. If a system of equations has infinitely many solutions, it's like having a party where everyone is wearing the same outfit! It's a consistent and dependent system, just like option C. Consistent, dependent.
I hope that clears things up for you! If not, feel free to ask more questions, and I'll keep the jokes coming!
For the first question, we can find the solutions by solving the system of equations. Here's how to do it:
1. Start by setting the two equations equal to each other:
x + 5 = -5x - 1
2. Simplify the equation by combining like terms:
6x = -6
3. Divide both sides of the equation by 6 to isolate x:
x = -1
4. Substitute the value of x (-1) back into one of the original equations to solve for y:
y = -1 + 5
y = 4
So the solution to the system of equations is x = -1 and y = 4. This means there is only one solution, which corresponds to option D (Two) being incorrect.
For the second question, we need to understand the terms given:
- Consistent: The system has at least one solution.
- Inconsistent: The system has no solution.
- Independent: Each equation provides new information, and the system has a unique solution.
- Dependent: One equation is a multiple or a linear combination of the other, resulting in infinitely many solutions.
Since we are looking for a system with infinitely many solutions, option C (Consistent, dependent) is the correct choice, and option D (Inconsistent) is incorrect.
I hope this clarifies your doubts!