Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match the systems of equations to their solutions.

1.
[tex]\[
\begin{aligned}
2x + y &= 12 \\
x &= 9 - 2y
\end{aligned}
\][/tex]

2.
[tex]\[
\begin{aligned}
y &= 11 - 2x \\
4x - 3y &= -13
\end{aligned}
\][/tex]

3.
[tex]\[
\begin{aligned}
x + 2y &= 9 \\
2x + 4y &= 20
\end{aligned}
\][/tex]

4.
[tex]\[
\begin{aligned}
y &= 10 + x \\
-3x + 3y &= 30
\end{aligned}
\][/tex]

5.
[tex]\[
\begin{aligned}
x + 3y &= 16 \\
2x - y &= 11
\end{aligned}
\][/tex]

6.
[tex]\[
\begin{aligned}
2x + y &= 11 \\
x - 2y &= -7
\end{aligned}
\][/tex]

Sagot :

GinnyAnswer
Of course! Let's match each system of equations with its respective solution:

1. System of Equations:
[tex]\[ \begin{aligned} 2x + y & = 12 \\ x & = 9 - 2y \end{aligned} \][/tex]
Solution: [tex]\(\{x: 5, y: 2\}\)[/tex]

Explanation: This system's solution is [tex]\(x = 5\)[/tex] and [tex]\(y = 2\)[/tex].

___

2. System of Equations:
[tex]\[ \begin{aligned} y & = 11 - 2x \\ 4x - 3y & = -13 \end{aligned} \][/tex]
Solution: [tex]\(\{x: 2, y: 7\}\)[/tex]

Explanation: This system's solution is [tex]\(x = 2\)[/tex] and [tex]\(y = 7\)[/tex].

___

3. System of Equations:
[tex]\[ \begin{aligned} y & = 10 + x \\ -3x + 3y & = 30 \end{aligned} \][/tex]
Solution: [tex]\(\{x = y - 10\}\)[/tex]

Explanation: This system has an infinite set of solutions given by the relationship [tex]\(x = y - 10\)[/tex].

___

4. System of Equations:
[tex]\[ \begin{aligned} x + 3y & = 16 \\ 2x - y & = 11 \end{aligned} \][/tex]
Solution: [tex]\(\{x: 7, y: 3\}\)[/tex]

Explanation: This system's solution is [tex]\(x = 7\)[/tex] and [tex]\(y = 3\)[/tex].

___

5. System of Equations:
[tex]\[ \begin{aligned} 2x + y & = 11 \\ x - 2y & = -7 \end{aligned} \][/tex]
Solution: [tex]\(\{x: 3, y: 5\}\)[/tex]

Explanation: This system's solution is [tex]\(x = 3\)[/tex] and [tex]\(y = 5\)[/tex].

___

For completeness, one system of equations does not have a solution listed here and is not part of the results. It is:

System (No Solution Listed):
[tex]\[ \begin{aligned} x + 2y & = 9 \\ 2x + 4y & = 20 \end{aligned} \][/tex]

To summarize the matching pairs:

1.
[tex]\[ \begin{aligned} 2x + y & = 12 \\ x & = 9 - 2y \end{aligned} \][/tex]
matches with [tex]\(\{x : 5, y : 2\}\)[/tex]

2.
[tex]\[ \begin{aligned} y & = 11 - 2x \\ 4x - 3y & = -13 \end{aligned} \][/tex]
matches with [tex]\(\{x : 2, y : 7\}\)[/tex]

3.
[tex]\[ \begin{aligned} y & = 10 + x \\ -3x + 3y & = 30 \end{aligned} \][/tex]
matches with [tex]\(\{x : y - 10\}\)[/tex]

4.
[tex]\[ \begin{aligned} x + 3y & = 16 \\ 2x - y & = 11 \end{aligned} \][/tex]
matches with [tex]\(\{x : 7, y : 3\}\)[/tex]

5.
[tex]\[ \begin{aligned} 2x + y & = 11 \\ x - 2y & = -7 \end{aligned} \][/tex]
matches with [tex]\(\{x : 3, y : 5\}\)[/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.