Math / Algebra

Question $\left\{\begin{array}{l} 5 y=15 x-40 \\ y=3 x-8 \end{array}\right.$
Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

Studdy Solution

STEP 1

What is this asking? We've got two equations, and we need to figure out if they have one solution, no solutions, or infinitely many solutions! Watch out! Don't just jump into calculations!
Make sure you understand what the equations represent before you start solving.

STEP 2

1. Simplify the first equation
2. Compare the equations

STEP 3

We're given $5y = 15x - 40$ .
Let's divide both sides of this equation by 5 to make it simpler!
We're doing this because it helps us isolate $y$ and see the relationship between $x$ and $y$ more clearly.
This gives us: $\frac{5y}{5} = \frac{15x - 40}{5}$ $y = \frac{15x}{5} - \frac{40}{5}$ $y = 3x - 8$

STEP 4

Whoa, check it out!
After simplifying the first equation, we get $y = 3x - 8$ , which is exactly the same as the second equation!
This means they represent the same line!

STEP 5

Since both equations represent the same line, any point that satisfies one equation will automatically satisfy the other.
That means there are tons of $x$ and $y$ values that work for both equations!

STEP 6

Because both equations are equivalent, there are infinitely many solutions!
So the answer is (C).

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Question $\left\{\begin{array}{l} 5 y=15 x-40 \\ y=3 x-8 \end{array}\right.$
Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

Studdy Solution

STEP 1

What is this asking? We've got two equations, and we need to figure out if they have one solution, no solutions, or infinitely many solutions! Watch out! Don't just jump into calculations!
Make sure you understand what the equations represent before you start solving.

STEP 2

1. Simplify the first equation
2. Compare the equations

STEP 3

STEP 4

Whoa, check it out!
After simplifying the first equation, we get $y = 3x - 8$ , which is exactly the same as the second equation!
This means they represent the same line!

STEP 5

Since both equations represent the same line, any point that satisfies one equation will automatically satisfy the other.
That means there are tons of $x$ and $y$ values that work for both equations!

STEP 6

Because both equations are equivalent, there are infinitely many solutions!
So the answer is (C).

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Question{5y=15x−40y=3x−8\left\{\begin{array}{l} 5 y=15 x-40 \\ y=3 x-8 \end{array}\right.{5y=15x−40y=3x−8​Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

Studdy Solution

STEP 1

What is this asking? We've got two equations, and we need to figure out if they have one solution, no solutions, or infinitely many solutions! Watch out! Don't just jump into calculations!Make sure you understand what the equations represent before you start solving.

STEP 2

1. Simplify the first equation2. Compare the equations

STEP 3

STEP 4

Whoa, check it out!After simplifying the first equation, we get y=3x−8y = 3x - 8y=3x−8, which is *exactly* the same as the second equation!This means they represent the same line!

STEP 5

Since both equations represent the same line, any point that satisfies one equation will *automatically* satisfy the other.That means there are tons of xxx and yyy values that work for both equations!

STEP 6

Because both equations are equivalent, there are **infinitely many solutions**!So the answer is (C).

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $\left\{\begin{array}{l} 5 y=15 x-40 \\ y=3 x-8 \end{array}\right.$
Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

What is this asking? We've got two equations, and we need to figure out if they have one solution, no solutions, or infinitely many solutions! Watch out! Don't just jump into calculations!
Make sure you understand what the equations represent before you start solving.

1. Simplify the first equation
2. Compare the equations

Whoa, check it out!
After simplifying the first equation, we get $y = 3x - 8$ , which is exactly the same as the second equation!
This means they represent the same line!

Since both equations represent the same line, any point that satisfies one equation will automatically satisfy the other.
That means there are tons of $x$ and $y$ values that work for both equations!

Because both equations are equivalent, there are infinitely many solutions!
So the answer is (C).