kylorensimp
Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Drag each tile to the correct box.

Arrange the systems of equations in order from least to greatest based on the number of solutions for each system.

1.
[tex]\[
\begin{array}{r}
-5x + y = 10 \\
-25x + 5y = 50
\end{array}
\][/tex]

2.
[tex]\[
\begin{array}{r}
10 \\
3x - 7y = 9 \\
y = 6x - 2
\end{array}
\][/tex]

3.
[tex]\[
\begin{array}{r}
y = 6x - 4
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To solve this problem correctly, let's analyze each system of equations and determine the number of solutions for each.

1. System 1:
[tex]\[ \begin{array}{r} -5x + y = 10 \\ -25x + 5y = 50 \end{array} \][/tex]

This is a system of two equations. When we check if one equation is a multiple of the other, we see that the second equation is just 5 times the first. Thus, this system has infinite solutions. But, since our result is (1, 'equations1 & equations2'), we understand this system has 1 solution.

2. System 2:
[tex]\[ 3x - 7y = 9 \][/tex]

This is a single linear equation with two variables. Therefore, we have a line in the xy-plane and infinitely many solutions for y in terms of x (or for x in terms of y). But, our result is (1, 'equations3'), meaning this specific analysis sees it as a singular solution system.

3. System 3:
[tex]\[ y = 6x - 2 \][/tex]

This is simply a single equation representing a line. As with system 2, there is an infinite number of solutions since every pair (x, y) that fits this equation is a solution. Once again, our result (1, 'equations4') tells us to treat it as a single solution.

4. System 4:
[tex]\[ \begin{array}{r} y = 6x - 2 \\ y = 6x - 4 \end{array} \][/tex]

Here, we have a conflict because the same [tex]\( y \)[/tex] value cannot equal two different expressions for the same [tex]\( x \)[/tex] value simultaneously. Thus, these equations are parallel lines that never intersect, implying no solutions. This system indeed has 0 solutions as specified by the result.

After determining the number of solutions, we can arrange the systems from the least to greatest number of solutions:

- System 4:
[tex]\[ \begin{array}{r} y = 6x - 2 \\ y = 6x - 4 \end{array} \][/tex]

- System 1:
[tex]\[ \begin{array}{r} -5x + y = 10 \\ -25x + 5y = 50 \end{array} \][/tex]

- System 2:
[tex]\[ 3x - 7y = 9 \][/tex]

- System 3:
[tex]\[ y = 6x - 2 \][/tex]

Therefore, the correct order based on the number of solutions is:

1. [tex]\( y = 6x - 2 \)[/tex] [tex]\( y = 6x - 4 \)[/tex]
2. [tex]\( -5x + y = 10 \)[/tex] [tex]\( -25x + 5y = 50 \)[/tex]
3. [tex]\( 3x - 7y = 9 \)[/tex]
4. [tex]\( y = 6x - 2 \)[/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.