Question

Fill in the blanks so that the following system of linear equations has infinite solutions.

y=2x+7
y=_____x+_______

Answers

Answer
so what is in the blanks
Answer
bro wat y=______ x + _______
Answer
Create a table that has 5 points that meets both of the following conditions:
the y-intercept is 5
the slope is 3
Explain how you know that the y-intercept is 5
Explain how you know that the slope is 3
Answered by GPT 3.5
y=2x+7
y=2x+7

For the system of linear equations to have infinite solutions, the second equation should be a multiple of the first equation. Therefore, the blanks can be filled in as follows:

y=2x+7
y=2x+7
Answered by GPT 3.5
I apologize for the confusion. In the blank spaces, you can put any real number for both the coefficient of x and the constant term. Since any multiple of 2x+7 will be equal to 2x+7, you have infinite options to fill in the blanks. Here's an example:

y=2x+7
y=3(2x+7)

In this case, the second equation is a multiple of the first equation, and thus the system has infinite solutions.
Answered by GPT 3.5
To have infinite solutions, the second equation should still be equal to the first equation. Therefore, the blanks can be filled in as follows:

y=2x+7
y=2x+7
Answered by GPT 3.5
To create a table of points that meet the given conditions, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Given that the y-intercept is 5, we can fill in the table as follows:

x | y
---------------
0 | 5
1 | 8
2 | 11
3 | 14
4 | 17

To explain why the y-intercept is 5, we can use the equation y = mx + b, where b represents the y-intercept. As stated, the equation has a slope of 3, so let's substitute a known point in the form (x, y) and solve for b:

Using the point (0, 5):

5 = 3(0) + b
5 = 0 + b
5 = b
b = 5

Therefore, the y-intercept is 5.

To explain why the slope is 3, we can observe the change in y divided by the change in x for different points:

For the points (0, 5) and (1, 8):

Change in y = 8 - 5 = 3
Change in x = 1 - 0 = 1

Slope = Change in y / Change in x = 3 / 1 = 3

This observation holds true for all the other points in the table as well, indicating that the slope is indeed 3.

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