Pregunta
How many solutions does this system have? \( \left\{\begin{array}{c}6 x-y=5 \\ 12 x-2 y=3\end{array}\right. \)
Ask by Lewis Warner. in the United States
Feb 05,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
El sistema no tiene solución.
Solución
Solve the system of equations \( 6x-y=5;12x-2y=3 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}6x-y=5\\12x-2y=3\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}y=-5+6x\\12x-2y=3\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(12x-2\left(-5+6x\right)=3\)
- step3: Simplify:
\(10=3\)
- step4: Calculate:
\(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \end{array}\right.\)
- step5: Rewrite:
\((x, y) \in \varnothing\)
El sistema de ecuaciones \( \left\{\begin{array}{c}6 x-y=5 \\ 12 x-2 y=3\end{array}\right. \) no tiene solución.
Revisado y aprobado por el equipo de tutoría de UpStudy
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Bonus Knowledge
To find out how many solutions the system has, we can simplify and analyze the equations. The second equation can be simplified by dividing all terms by 2, leading to \(6x - y = 1.5\). Now, we have the system: 1. \(6x - y = 5\) 2. \(6x - y = 1.5\) Since both expressions equal \(6x - y\) but have different constants (5 and 1.5), the lines represented by these equations are parallel and will never intersect. This implies that there is no solution to this system; it has zero solutions.
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