Ask a New Question
Menu

se the image to answer the question.

A coordinate plane's x-axis ranges from negative 5 to 5 and its y-axis ranges from negative 3 to 7, both in 1-unit increments. A parabola and a line are plotted. The line and parabola intersect at two points. 1 point of intersection is in quadrant 1 and the other is in quadrant 2.

Which of the following shows the solution(s) for this system of equations?

(1 point)
Responses

(−2,4) and (2,4)
left parenthesis negative 2 comma 4 right parenthesis and left parenthesis 2 comma 4 right parenthesis

There are no solutions.
There are no solutions.

(−3,0) and (3,0)
left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 3 comma 0 right parenthesis

(0,8)

3 answers

To solve this problem, we need to identify the points of intersection between the parabola and the line as described.

Given the information:

  • The parabola and the line intersect at two points—one in quadrant 1 and one in quadrant 2.
  • Quadrant 1 is where both x and y values are positive (x > 0, y > 0), and quadrant 2 is where x is negative and y is positive (x < 0, y > 0).

Considering the provided response options:

  1. (−2, 4) and (2, 4) - The first point is in quadrant 2 and the second one is in quadrant 1 (valid).
  2. No solutions - This option does not apply since intersections are given.
  3. (−3, 0) and (3, 0) - Both points are on the x-axis, which would not be valid as both have y = 0.
  4. (0, 8) - This point is above the y-axis in quadrant 1 but doesn't provide an intersection in quadrant 2.

The first option shows one intersection in quadrant 2 (−2, 4) and the other in quadrant 1 (2, 4), which matches the information given in the prompt.

Therefore, the correct response is: (−2, 4) and (2, 4).

Which equation describes an infinite solution system with the equation y=4x−3 ?(1 point)
Responses

2y−8x=6
2 y minus 8 x equals 6

2y−8x=−6
2 y minus 8 x equals negative 6

−2y+8x=−6
negative 2 y plus 8 x equals negative 6

2y+8x=−6

To find an equation that describes an infinite solution system with the equation \( y = 4x - 3 \), we need to determine which of the given options corresponds to this line. Infinite solutions occur when two equations represent the same line, meaning they are equivalent.

Starting with the equation \( y = 4x - 3 \):

  1. Rearrange to standard form:
    Multiply both sides by 2 to manipulate it into the format of the options. \[ 2y = 8x - 6 \quad \Rightarrow \quad 2y - 8x = -6 \]

Now, we will compare this with the options given:

  1. Option 1: \( 2y - 8x = 6 \) - Not equivalent (different constant).
  2. Option 2: \( 2y - 8x = -6 \) - Equivalent! (correct, as derived).
  3. Option 3: \(-2y + 8x = -6\) - Not equivalent (note the signs).
  4. Option 4: \( 2y + 8x = -6 \) - Not equivalent (again, different constant and signs).

Thus, the correct option that describes an infinite solution system with the equation \( y = 4x - 3 \) is:

\( 2y - 8x = -6 \).