How many solutions does the system of equations have?

y=6x+2 and 3y-18x=12
one
two
infinitely many
none

How many solutions does the system of equations have?
x-3y=15 and 3x-9y=45
one
two
infinitely many
none

How many solutions does the system of equations have?
y-5x=-6 and 3y-15x= -12
one
two
infinitely many
none

please help 3 days until the semester is over. please help me

Bro i have 3 days and all my exams left 😭😭😭

i can't think of anything when i have 3 days left and 2 exams left

Thx for the help and good luck on exams

To determine the number of solutions for a system of equations, you can use a method called elimination or substitution. I'll guide you through the process step by step for each question:

1. System of Equations:
y = 6x + 2
3y - 18x = 12

First, we'll check if the second equation can be simplified. Divide both sides by 3 to obtain:
y - 6x = 4

Now, let's compare the simplified second equation with the first equation to see if they are equivalent. In this case, the equations are not equivalent because the coefficients of x and y don't match (6 and 1 in the first equation, and -6 and 1 in the second equation).

Since the two equations do not represent the same line, we can conclude that the system of equations has one solution.

2. System of Equations:
x - 3y = 15
3x - 9y = 45

Let's simplify the second equation by dividing both sides by 3:
x - 3y = 15

Now, we can compare the simplified second equation with the first equation. The simplified second equation is equivalent to the first equation when multiplied by 3. This means that both equations represent the same line.

Since the two equations represent the same line, the system of equations has infinitely many solutions.

3. System of Equations:
y - 5x = -6
3y - 15x = -12

We'll simplify the second equation by dividing both sides by 3:
y - 5x = -6

Comparing this simplified second equation with the first equation, we can see that they are equivalent since the coefficients of x and y match (5 in both equations).

Since the two equations represent the same line, the system of equations has infinitely many solutions.

In summary:
1. The system of equations has one solution.
2. The system of equations has infinitely many solutions.
3. The system of equations has infinitely many solutions.

I hope this explanation helps! If you have any more questions, feel free to ask. Good luck with your semester.

2. Multiply the 1st Eq by 3 and you'll notice that the Eqs are identical and have infinite solutions.

What do you think?

1. Eq1: Y = 6x + 2.

Eq2: - 18x + 3y = 12.
m1 = 6.
m2 = -A/B = 18/3 = 6.
The Eqs have equal slopes and are, therefore, parallel and do not intersect:
No solution.

2. Same procedure as #1.

3. Standard Form: -5x + y = -6, and -15x + 3y = -12.
Same procedure as #1.