Question

Use the image to answer the question.

A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 3.
Review the graphs of a system of two linear equations in two variables: x−5y=7 and 3x−2y=−4 . Find the solution to both equations.
The intersection point is _____.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The intersection point is (-2, -1).

Answer 2

Use the image to answer the question.

A coordinate plane with four quadrants shows the x-axis ranging from negative 10 to 10 in increments of 1 and the y-axis ranging from negative 5 to 15 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is y equals x plus 5. The equation of the dotted line is 4 x plus 3 y equals 15. The intersection point of both lines is shown at 0 on the x-axis and positive 5 on the y-axis.
Review the graphs of a system of two linear equations in two variables: 4x+3y=15 and y=x+5 . Find the solution to both equations.
The intersection point is _____.

Answer 3

[AI-generated answer — Bot GPT 3.5]

The intersection point is (0, 5).

Answer 4

Use the image to answer the question.

A coordinate plane with four quadrants shows the x-axis ranging from negative 5 to 15 in increments of 1, and the y-axis ranging from negative 10 to 10 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is y equals x minus 6. The equation of the dotted line is y equals negative x plus 4. The intersection point of both lines is shown at positive 5 on the x-axis and negative 1 on the y-axis in quadrant 4.
Review the graphs of a system of two linear equations in two variables: y=x−6 and y=−x+4. Find the solution to both equations.
The intersection point is _____.

Answer 5

[AI-generated answer — Bot GPT 3.5]

The intersection point is (5, -1).

Answer 6

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals negative x plus 6. The equation of the dotted line is y equals x plus 2. The lines intersect at left parenthesis 2 comma 4 right parenthesis which is not plotted as a point.
Estimate the intersection point of the graphs of the following linear equations in two variables.
y = x + 2
y = −x + 6

Answer 7

[AI-generated answer — Bot GPT 3.5]

Since the given intersection point is not plotted on the graph, you can consider the point (2,4) as the intersection. So, the estimated intersection point is (2,4).

Answer 8

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals negative x plus 7. The equation of the dotted line is y equals 4 x minus 3. The lines intersect at left parenthesis 2 comma 5 right parenthesis which is not plotted as a point.
Estimate the intersection point of the graphs of the following linear equations in two variables.
y = −x + 7
y = 4x − 3

Answer 9

[AI-generated answer — Bot GPT 3.5]

Since the given intersection point (2, 5) is not plotted on the graph, you can consider it as the estimated intersection point. Therefore, the estimated intersection point of the two linear equations y = −x + 7 and y = 4x − 3 is (2, 5).

Answer 10

Use the image to answer the question.

A coordinate plane with four quadrants shows the x-axis ranging from negative 5 to 15 in increments of 1 and the y-axis ranging from negative 10 to 10 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is 2 x plus y equals 15. The equation of the dotted line is y equals negative x plus 5. The intersection of both lines is shown at positive 10 on the x-axis and negative 5 on the y-axis in quadrant 4.
Find the coordinates of the intersection point that solves the system of these two linear equations in two variables: 2x + y = 15 and y = −x + 5.

A. (10,−5)

B. (−5, 10)

C. (5,−10)

D. (−10, 5)

Answer 11

[AI-generated answer — Bot GPT 3.5]

The coordinates of the intersection point are (10, -5).

Therefore, the correct option is:

A. (10,−5)