Which graph shows the solution of −3x−y=3 and y=−3x+4 ?(1 point) Responses Image with alt text: Two intersecting lines are graphed across a coordinate plane. Image with alt text: Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid. Image with alt text: Two intersecting lines are graphed across a coordinate plane. Image with alt text: Two intersecting lines are graphed across a coordinate plane. Skip to navigation

Answer 1

To determine which graph represents the solutions of the equations \(-3x - y = 3\) and \(y = -3x + 4\), let's analyze both equations:

1. Rearranging the first equation: \(-3x - y = 3\)

   Add \(3x\) to both sides: \(-y = 3 + 3x\)

   Multiply by -1: \(y = -3x - 3\)

   This is the slope-intercept form with a slope of -3 and a y-intercept of -3.

2. The second equation is already in slope-intercept form: \(y = -3x + 4\)

   Here, the slope is also -3, but the y-intercept is 4.

Analysis of the Lines:

• Both equations have the same slope of -3, which means they are parallel lines.
• Since the y-intercepts are different (-3 for the first line and +4 for the second line), the lines will never intersect.

Conclusion:

The correct graph that represents these two lines is the one showing two parallel lines, as they will not intersect (there are no solutions to the system of equations).

So, you would select the graph labeled as "Two parallel lines are graphed across a coordinate plane."

Answer 2

Use the image to answer the question. In math class, Emma and Angelle pair as a group. Emma’s task is to graph (7/2)x−(9/2)=2y and Angelle’s task is to graph 4y=7x−9 . After they complete their graphs, they compare their work. They both get exactly the same graph. What is the solution of (7/2)x−(9/2)=2y and 4y=7x−9 ? (1 point) Responses no solution no solution (1.286,0) left parenthesis 1.286 comma 0 right parenthesis an infinite number of solutions an infinite number of solutions (1.286,0) and (0,−2.25) left parenthesis 1.286 comma 0 right parenthesis and left parenthesis 0 comma negative 2.25 right parenthesis Skip to navigation

Answer 3

To find the solution of the equations \((7/2)x - (9/2) = 2y\) and \(4y = 7x - 9\), let's rewrite both equations in a standard form and analyze them.

1. Rearranging the first equation: \[ (7/2)x - (9/2) = 2y \] Multiply through by 2 to eliminate the fractions: \[ 7x - 9 = 4y \] Rearranging gives: \[ 4y = 7x - 9 \]

2. The second equation is already in the form: \[ 4y = 7x - 9 \]

Analysis:

Since both equations simplify to the same equation \(4y = 7x - 9\), they represent the same line. Therefore, every point on this line is a solution to both equations, which means there are infinitely many solutions.

Conclusion:

The correct answer is an infinite number of solutions.

Answer 4

Use the table to answer the question. x-value y-value if y=2x−5 y-value if y=x−3 0 −5 −3 1 −3 −2 2 −1 −1 3 1 0 Jian made a table showing some x- and y-values in a system of equations. Use his table to identify the solution for the system. (1 point) Responses There is no solution. There is no solution. (2,−1) left parenthesis 2 comma negative 1 right parenthesis (3,0) left parenthesis 3 comma 0 right parenthesis There is an infinite number of solutions.

Answer 5

To solve the problem, let's analyze the equations given:

1. Equation 1: \(y = 2x - 5\)
2. Equation 2: \(y = x - 3\)

Now, let's evaluate the provided table for corresponding x-values and the calculated y-values for both equations:

• For \(x = 0\):

  • From \(y = 2(0) - 5\): \(y = -5\)
  • From \(y = 0 - 3\): \(y = -3\)

• For \(x = 1\):

  • From \(y = 2(1) - 5\): \(y = -3\)
  • From \(y = 1 - 3\): \(y = -2\)

• For \(x = 2\):

  • From \(y = 2(2) - 5\): \(y = -1\)
  • From \(y = 2 - 3\): \(y = -1\)

• For \(x = 3\):

  • From \(y = 2(3) - 5\): \(y = 1\)
  • From \(y = 3 - 3\): \(y = 0\)

Finding the Solution:

Now, we check for matching pairs of (x, y) between both equations:

• When \(x = 0\): y-values are -5 and -3 (not a solution).
• When \(x = 1\): y-values are -3 and -2 (not a solution).
• When \(x = 2\): both equations yield \(y = -1\). This means \((2, -1)\) is a solution.
• When \(x = 3\): y-values are 1 and 0 (not a solution).

Conclusion:

The only pair that satisfies both equations in the table is \((2, -1)\).

Thus, the answer is: \((2, -1)\).

Answer 6

Use the image to answer the question. Which of the following shows the solution(s) for this system of equations? (1 point) Responses There are no solutions. There are no solutions. (−2,4) and (2,4) left parenthesis negative 2 comma 4 right parenthesis and left parenthesis 2 comma 4 right parenthesis (0,8) left parenthesis 0 comma 8 right parenthesis (−3,0) and (3,0) left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 3 comma 0 right parenthesis Skip to navigation

Answer 7

To determine the solutions for the system of equations shown in the image that you referenced, we would typically analyze the equations to find any intersection points (solutions) or determine if there are no solutions (if the lines are parallel) or infinitely many solutions (if the lines overlap).

Since I cannot see the image you're referencing, I'll provide a general framework on how to arrive at the answer based on typical scenarios:

1. No Solutions: If the two lines are parallel (same slope, but different y-intercepts), they will never intersect, so there are no solutions.

2. Infinitely Many Solutions: If the two equations represent the same line (identical equations), there will be infinitely many solutions because every point on that line is a solution.

3. A Single Point as Solution: If the two lines intersect at a unique point, that point is the solution to the system.

Checking the Options Given:

Given your options, you'll want to see if:

• The points \((-2, 4)\) and \( (2, 4)\) are shown as intersections of two lines on the graph.
• The point \((0, 8)\) is shown as an intersection.
• The points \((-3, 0)\) and \( (3, 0)\) are shown as intersections.

How to Proceed:

• If you can visually confirm where the lines intersect using the graph, identify the coordinates at which they intersect.
• If there is more than one intersection point, look for responses that correspond to those solutions.
• If you're unable to identify intersections, confirm if the lines are parallel (leading to "no solutions") or identical (leading to "an infinite number of solutions").

Conclusion:

Without the ability to view the image, I would suggest comparing the coordinates in the response options with the graphical intersections of the lines presented in the image. Based on what you see, select the response that corresponds to the correct intersection(s) or relationship (parallel, identical) between the equations.