Question
Solve the system by the method of your choice. \( \begin{array}{r}4 x=y-2 \\ 4 x-y=9\end{array} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \). (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.
Ask by Bond Fuentes. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There is no solution.
Solution
Solve the system of equations \( 4x=y-2;4x-y=9 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}4x=y-2\\4x-y=9\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}4x=y-2\\y=-9+4x\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(4x=-9+4x-2\)
- step3: Simplify:
\(4x=-11+4x\)
- step4: Cancel equal terms:
\(0=-11\)
- step5: The statement is false:
\(x \in \varnothing \)
- step6: Calculate:
\(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \end{array}\right.\)
- step7: Rewrite:
\((x, y) \in \varnothing\)
The system of equations \( \begin{array}{r}4x=y-2 \\ 4x-y=9\end{array} \) has no solution. Therefore, the correct choice is:
C. There is no solution.
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Simplify this solution Mind Expander
Let's solve the system of equations step by step. 1. From the first equation \(4x = y - 2\), we can express \(y\) in terms of \(x\): \[ y = 4x + 2 \] 2. Next, we substitute \(y\) in the second equation \(4x - y = 9\): \[ 4x - (4x + 2) = 9 \] Simplifying, we have: \[ 4x - 4x - 2 = 9 \] \[ -2 = 9 \] Since the above statement is false, it indicates that there are no values for \(x\) and \(y\) that satisfy both equations simultaneously. Therefore, the answer is: C. There is no solution.
