Question

Quiz
Question 1 (1 point)
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y=1/3x-2
y=-x+2

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What is the solution to the following systems of equation?



Question 1 options:

(3, -1)


No Solutions


Infinite Solutions


(-1, 3)

Question 2 (1 point)
Saved
y=-1/2x+3
y=5
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What is the solution to the following systems of equation?



Question 2 options:

No Solutions


(5, -4)


Infinite Solutions


(-4, 5)

Question 3 (1 point)
Saved

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Willa graphed a system of equations on the same coordinate grid. The equations had the same slope, but different y-intercepts. Which must be true?

Question 3 options:

The system has no solution.


The system has one solution.


The system has infinitely many solutions.


There is not enough information to tell.

Question 4 (1 point)

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Which of the following would result in a system of equations that is inconsistent?

Question 4 options:

A pair of lines that are parallel.


A pair of lines that are the same.


A pair of lines that intersect in one and only one spot.

Question 5 (1 point)

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Ashton graphed a system of equations with infinitely many solutions. What must be true about the equations of the lines?

Question 5 options:

They have different y-intercepts.


The have the same slope.


The lines are parallel.


All off the above.


3 of 5 questions saved
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Answer 1

Here are the answers to your quiz questions:

### Question 1:
To solve the system of equations:
1. \(y = \frac{1}{3}x - 2\)
2. \(y = -x + 2\)

Set the equations equal to each other:
\[\frac{1}{3}x - 2 = -x + 2\]

Multiply everything by 3 to eliminate the fraction:
\[x - 6 = -3x + 6\]

Combine like terms:
\[4x = 12\]
\[x = 3\]

Now substitute \(x = 3\) back into one of the equations to find \(y\):
\[y = -3 + 2 = -1\]

So, the solution is **(3, -1)**.

### Question 2:
To solve the system of equations:
1. \(y = -\frac{1}{2}x + 3\)
2. \(y = 5\)

Set them equal to each other:
\[-\frac{1}{2}x + 3 = 5\]

Subtract 3 from both sides:
\[-\frac{1}{2}x = 2\]

Multiply by -2:
\[x = -4\]

Now substitute \(x = -4\) back into the equation \(y = 5\):
So the solution is **(-4, 5)**.

### Question 3:
If Willa graphed a system of equations with the same slope but different y-intercepts, it means the lines are parallel and will never intersect. Therefore, the system has no solution.
The answer is **The system has no solution.**

### Question 4:
A system of equations is inconsistent if the lines are parallel. Parallel lines have the same slope but different y-intercepts. Therefore, the answer is **A pair of lines that are parallel.**

### Question 5:
If a system of equations has infinitely many solutions, it means the equations represent the same line (i.e., they have the same slope and y-intercept). So, they must have the same slope.
The answer is **They have the same slope.**

### Summary of Answers:
1. (3, -1)
2. (-4, 5)
3. The system has no solution.
4. A pair of lines that are parallel.
5. They have the same slope.