Question

2x+y=6

8x+4y=8
What is the first step in determining the number of soultions in this system of equations?
A.find x and re-write
B.find y and re-write
C.re-write in y-intercept format

Answer 1

[AI-generated answer — Bot GPT 3.5]

The first step in determining the number of solutions in this system of equations is to rewrite the equations in a standard form. Therefore, the correct answer is A: find x and re-write.

Answer 2

How do you write 8x+4y=8 in y-intercept format?

A. -4y=8 +18 so y=4x+18
B. 4y=-8x+8 so y=-2x+2
C. This cannot be written in y-intercet format.

Answer 3

[AI-generated answer — Bot GPT 3.5]

To write the equation 8x + 4y = 8 in y-intercept format, we need to isolate y.

First, we subtract 8x from both sides:
4y = -8x + 8

Then, divide by 4 to solve for y:
y = -2x + 2

Therefore, the y-intercept format of the equation 8x + 4y = 8 is y = -2x + 2.

So the correct answer is B: y = -2x + 2.

Answer 4

How many systems of equations are there when the equations have the same slope and different y-intercepts?

A.one sultion since there are many lines.
B.infinte since the lines intersect
C.No solution, the lines are parallel

Answer 5

[AI-generated answer — Bot GPT 3.5]

When two equations have the same slope and different y-intercepts, the lines are parallel to each other and will never intersect. Therefore, the correct answer is:

C. No solution, the lines are parallel.

Answer 6

What is the y-intercept in this equation: y=2x+1

A.2
B.4
C.1

Answer 7

[AI-generated answer — Bot GPT 3.5]

In the equation y = 2x + 1, the y-intercept is the point where the line intersects the y-axis. Since the y-intercept occurs when x = 0, we can plug in x = 0 into the equation to find the y-intercept.

y = 2(0) + 1
y = 0 + 1
y = 1

Therefore, the y-intercept in the equation y = 2x + 1 is y = 1.

So, the correct answer is: C. 1

Answer 8

How many solutions can be found when both equations have different slopes?

A.only one possible solution
B.no solutions
C.infinite solutions

Answer 9

[AI-generated answer — Bot GPT 3.5]

When both equations have different slopes, they will intersect at a single point which is the solution to the system of equations. Thus, the correct answer is:

A. only one possible solution

Answer 10

After re-writing 2 equations into y-intercept form, the equations are the same (with the same slope amd y -intercept.) How many possible solutions can there be for these systems of equations?

A.one
B.infinie
C.zero

Answer 11

[AI-generated answer — Bot GPT 3.5]

If after re-writing two equations into y-intercept form, they are the same (with the same slope and y-intercept), then the two lines will coincide and overlap each other. This means that there are infinite solutions because every point on one line is also on the other line.

So, the answer is:

B. infinite.