kylorensimp
Answered

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Select all the systems of equations that have no solution.

[tex]\[
\begin{aligned}
x + 4y &= 23 \\
-3x &= 12y + 1
\end{aligned}
\][/tex]

[tex]\[
\begin{aligned}
2x + 4y &= 22 \\
-x &= 2y - 11
\end{aligned}
\][/tex]

[tex]\[
\begin{aligned}
2x + y &= 17 \\
-4x &= 2y - 34
\end{aligned}
\][/tex]

[tex]\[
\begin{aligned}
3y &= 10 - x \\
2x + 6y &= 7
\end{aligned}
\][/tex]

[tex]\[
\begin{aligned}
2x + y &= 15 \\
x &= 15 - 2y
\end{aligned}
\][/tex]

[tex]\[
\begin{aligned}
y &= 13 - 2x \\
4x - y &= -1
\end{aligned}
\][/tex]

Sagot :

GinnyAnswer
To determine which systems of equations have no solution, we need to analyze each system one-by-one. Let's verify:

1. System 1:
[tex]\[ \begin{aligned} x + 4y & = 23 \\ -3x - 12y & = -1 \end{aligned} \][/tex]

After examination, this system has no solution.

2. System 2:
[tex]\[ \begin{aligned} 2x + 4y & = 22 \\ -x - 2y & = 11 \end{aligned} \][/tex]

After examination, this system has no solution.

3. System 3:
[tex]\[ \begin{aligned} 2x + y & = 17 \\ -4x - 2y & = -34 \end{aligned} \][/tex]

After examination, this system has a solution.

4. System 4:
[tex]\[ \begin{aligned} 3y & = 10 - x \\ 2x + 6y & = 7 \end{aligned} \][/tex]

After examination, this system has no solution.

5. System 5:
[tex]\[ \begin{aligned} 2x + y & = 15 \\ x & = 15 - 2y \end{aligned} \][/tex]

After examination, this system has a solution.

6. System 6:
[tex]\[ \begin{aligned} y & = 13 - 2x \\ 4x - y & = -1 \end{aligned} \][/tex]

After examination, this system has a solution.

Based on this detailed analysis, the systems of equations that have no solution are:

1. System 1:
[tex]\[ \begin{aligned} x + 4y & = 23 \\ -3x - 12y & = -1 \end{aligned} \][/tex]

2. System 2:
[tex]\[ \begin{aligned} 2x + 4y & = 22 \\ -x - 2y & = 11 \end{aligned} \][/tex]

4. System 4:
[tex]\[ \begin{aligned} 3y & = 10 - x \\ 2x + 6y & = 7 \end{aligned} \][/tex]
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