How many solutions does the system have?

Question

How many solutions does the system have?

y - 5x = -6
3y - 15x = -12

A) infinitely many solutions
B) no solution
C) two solutions
D) one solution

Answer 1

3 y - 15 x = -18

3 y - 15 x = -12

These are two parallel lines that never intersect. There are therefore no solution points.

Answer 2

Well, let me put on my clown shoes and entertain you with a mathematical joke. Why did the math textbook look so sad? Because it had too many problems!

But to answer your question, we can solve the system of equations to determine the number of solutions. Let's start by rearranging the first equation:

y = 5x - 6

Now substitute this expression for y in the second equation:

3(5x - 6) - 15x = -12

Simplify the equation:

15x - 18 - 15x = -12

Uh-oh! We ended up with -18 = -12, which is not a true statement.

So, there are no values that satisfy both equations simultaneously. Therefore, the system has...

B) no solution!

Remember, even when math seems serious, it's okay to laugh and have fun with it!

Answer 3

To determine the number of solutions for the system, we can use the concept of elimination or substitution.

Let's solve the system using elimination:

First, we'll multiply the first equation by 3 to make the coefficients of y the same:

3(y - 5x) = 3(-6)
3y - 15x = -18

Now we can compare this equation to the second equation:

3y - 15x = -18
3y - 15x = -12

The two equations are identical, which means they represent the same line. Therefore, the system has infinitely many solutions.

So, the correct answer is A) infinitely many solutions.

Answer 4

To determine how many solutions the system of equations has, we need to solve the system and analyze the result.

Let's start by solving the given system of equations:

1) y - 5x = -6
2) 3y - 15x = -12

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

First, let's multiply equation 1 by 3 to have the same coefficient for y:
3 * (y - 5x) = 3 * (-6)
3y - 15x = -18

Now we have two equations with the same coefficient for y:

3y - 15x = -18
3y - 15x = -12

If we subtract equation 2 from equation 1, we get:

(3y - 15x) - (3y - 15x) = -18 - (-12)
0 = -18 + 12
0 = -6

This equation simplifies to 0 = -6, which is always false. Since this statement is not true, it means that the system of equations is inconsistent and has no solution.

Therefore, the answer is:

B) no solution