Requesting help.

(I must reckon, that X is a variable, and y is y-intercept)

Q: Try to use the substitution method to solve the the linear system y=3x an y=3x-7. What do you notice?
A) What happens when you graph it?
B) Explain why there is no solution.

And...

Q: Try to use the substitution method to solve the the linear system 3y-6x=15 an y=2x+5. What do you notice?
A) What happens when you graph it?
B) Explain why there is more than one solution?

My highest gratitude for who ever could help! It is critical that these answers are correct.

You need to do the exercises. You are being asked to do some thinking about what a solution.

When do lines cross, and when do they not is what the exercises are trying to develope in your thinking.

algebra is malaking bra

Sure, I can help you with these questions. Let's start with the first one.

Q: Try to use the substitution method to solve the linear system y=3x and y=3x-7. What do you notice?

To use the substitution method, we need to substitute one equation into the other. Let's substitute y=3x into y=3x-7:

3x = 3x - 7

Since both sides have 3x, we can subtract 3x from both sides:

0 = -7

Here, we have a contradiction. The equation 0 = -7 is not true, which means there is no solution to the system.

Now, let's move to the second question.

Q: Try to use the substitution method to solve the linear system 3y-6x=15 and y=2x+5. What do you notice?

To use the substitution method, we'll substitute y=2x+5 into 3y-6x=15:

3(2x + 5) - 6x = 15

Distribute the 3 to 2x and 5:

6x + 15 - 6x = 15

The x terms cancel out:

15 = 15

Here, we have an equation that is always true, which means the system has infinitely many solutions. When you graph the two equations, you will see that the lines are actually the same line. The two equations represent the same line, so there are infinite points of intersection, hence infinite solutions.

I hope this helps! If you have any more questions, feel free to ask.

Sure, I can help you with these questions! Let's start with the first one:

Q: Try to use the substitution method to solve the linear system y=3x and y=3x-7. What do you notice?

To solve this using the substitution method, we substitute the value of y from one equation into the other equation. Here's how it works:

Step 1: Since both equations have y equal to something, we can equate the right-hand sides of the equations:

- From the first equation: y = 3x
- Substitute this value of y into the second equation: 3x = 3x - 7

Step 2: Now we can try to solve for x. Let's simplify the equation:

3x - 3x = -7
0 = -7

Step 3: By solving the equation, we find that 0 is equal to -7. This is not possible since 0 cannot equal -7.

So, what do we notice? We notice that the equations are inconsistent and have no solution.

Now let's move on to the second question:

Q: Try to use the substitution method to solve the linear system 3y-6x=15 and y=2x+5. What do you notice?

Again, we'll use the substitution method to solve this system of equations:

Step 1: We take the value of y from the second equation and substitute it into the first equation:

- From the second equation: y = 2x + 5
- Substitute this value of y into the first equation: 3(2x + 5) - 6x = 15

Step 2: Simplify the equation by distributing and combining like terms:

6x + 15 - 6x = 15
15 = 15

Step 3: By solving the equation, we find that 15 is equal to 15. This means that the equations are consistent and have infinitely many solutions.

What do we notice? We notice that the equations are dependent on each other and have more than one solution.

As for graphing, when we graph the first system of equations, y=3x and y=3x-7, we will see two parallel lines that never intersect. This confirms our conclusion that there is no solution.

Similarly, when we graph the second system of equations, 3y-6x=15 and y=2x+5, we will see two lines that are coincident or overlap each other. This confirms our conclusion that there are infinitely many solutions.

I hope this helps! Let me know if you have any further questions.