Question

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 4 x minus 10. The equation of the dotted line is y equals negative 2 x plus 8. The intersection point of both lines is shown at positive 3 on the x-axis and positive 2 on the y-axis in quadrant 1. Review the graphs of a system of these two linear equations in two variables: y=4x−10 and y=−2x+8 Find the solution of the system. (1 point) The solution of the system of equations is ().

Answer 1

[AI-generated answer — Bot GPT 3.5]

(3, 2)

Answer 2

Use the image to answer the question. An illustration of a coordinate plane with four quadrants shows the x axis extending from negative 10 to 10 in increments of 1 and the y axis extending from negative 5 to 15 in increments of 1. A solid line and a dotted line with arrows at both end intersect each other. The equation of the solid line is y equals one half x plus 6. The equation of the dotted line is y equals 2 x plus 3. The lines intersect at left parenthesis 2 comma 7 right parenthesis which is not plotted as a point. Estimate the solution to the system of these linear equations based on the graph y=2x+3 y=12x+6 (1 point) Responses(−2, 7) left parenthesis negative 2 comma 7 right parenthesis (2, 7) left parenthesis 2 comma 7 right parenthesis (7, 2) left parenthesis 7 comma 2 right 2, −7)

Answer 3

[AI-generated answer — Bot GPT 3.5]

(2, 7)

Answer 4

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 3 x minus 2. The equation of the dotted line is y equals negative x plus 6. The lines intersect at left parenthesis 2 comma 4 right parenthesis which is not plotted as a point. Estimate the solution to the system of these linear equations based on the graph. y=−x+6 y=3x−2

Answer 5

[AI-generated answer — Bot GPT 3.5]

The solution of the system of equations is (2, 4) or the point where the lines intersect appears to be at (2, 4).

Answer 6

Determine the number of solutions to this system of linear equations:2x+y=6 4x+2y=8

Answer 7

[AI-generated answer — Bot GPT 3.5]

These two equations are actually equivalent, meaning that the second equation is just twice the first one. This means that the two lines represented by these equations are the same line; they coincide with each other.

Since the lines are the same, there are infinite solutions to this system, as any point on the line given by the first equation will satisfy both equations.

Answer 8

Solve the system of equations.

4x−8y=−36
−6x+y=32

Answer 9

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method here.

The system of equations is:
4x - 8y = -36
-6x + y = 32

We can multiply the second equation by 8 to match the coefficient of y in both equations:
-6x + y = 32
=> 8(-6x + y) = 8(32)
-48x + 8y = 256

Now we have:
4x - 8y = -36
-48x + 8y = 256

Adding these two equations together to eliminate y:
4x - 8y + (-48x + 8y) = -36 + 256
-44x = 220
x = 220 / -44
x = -5

Now, substitute x = -5 back into the second equation:
-6(-5) + y = 32
30 + y = 32
y = 32 - 30
y = 2

Therefore, the solution to the system of equations is x = -5 and y = 2, or the point of intersection is (-5, 2).