Pregunta
upstudy study bank question image url

a) \( \left\{\begin{array}{l}4 m+2 m=6 \\ 2 m-2 m=4\end{array}\right. \)

Ask by Kelley Ross. in Angola
Jan 23,2025

Solución de tutoría real

Respuesta verificada por el tutor

Responder

O sistema de equações não tem solução porque a segunda equação resulta em uma contradição.

Solución

a) Resolver o sistema de equações: \[ \left\{ \begin{array}{l} 4m + 2m = 6 \\ 2m - 2m = 4 \end{array} \right. \] **Passo 1:** Simplificar a primeira equação. \[ 4m + 2m = 6 \\ 6m = 6 \\ m = \frac{6}{6} \\ m = 1 \] **Passo 2:** Substituir \( m = 1 \) na segunda equação. \[ 2m - 2m = 4 \\ 2(1) - 2(1) = 4 \\ 2 - 2 = 4 \\ 0 = 4 \] **Conclusão:** A segunda equação resulta em uma contradição (\( 0 = 4 \)), o que significa que não há nenhum valor de \( m \) que satisfaça ambas as equações simultaneamente. Portanto, o sistema é **inconsistente** e **não possui solução**.

Revisado y aprobado por el equipo de tutoría de UpStudy

error msg
Explicar
Simplifique esta solución

Extra Insights

Let's break it down! In the first equation, \(4m + 2m = 6\), if we combine like terms, we get \(6m = 6\). Dividing both sides by 6 gives us \(m = 1\). Now, onto the second equation: \(2m - 2m = 4\). Here, \(2m - 2m\) simplifies to \(0 = 4\), which is a contradiction. This means the second equation has no valid solutions when \(m = 1\) from the first equation. So, the first equation gives us a value for \(m\), but the second one shows a contradiction, indicating that this system has no solution. What a twist!

Latest Algebra Questions

Point-Slope Form For each row, you and your partner will answer the question shown. Begin by reading each scenario. Using point-slope form, write the equation of the line that describes this scenario. Then, rewrite the equation in slope-intercept form. You and your partner should get the same answer for slope-intercept form. If you disagree, work together to reach an agreement. Partner A 1. In order to enter the state fair, there is an admission cost. Each game is \( \$ 3 \). Steven went to the state fair, played 4 games and spent a total of \( \$ 20 \) on admission and games. 2. At a chili cook off, people pay \( \$ 0.50 \) for each sample bowl of chili. The total cost was \( \$ 4.50 \) for 3 bowls of chili. 3. CJ loves Girl Scout cookies. He eats 3 cookies per hour. After 5 hours, there are 24 cookies left in the box. 4. An oil tank is being filled at a constant rate of 0.2 gallons per minute. After 10 minutes, there are 5 gallons of oil in the tank. 5. The total cost of renting a vacation home includes a deposit and a daily rental fee of \( \$ 125 \). A family rents a vacation home for 5 days and pays \( \$ 700 \). Partner B 1. In order to enter the state fair, there is an admission cost. Each game is \( \$ 3 \). Steven went to the state fair, played 10 games and spent a total of \( \$ 38 \) on admission and games. 2. At a chili cook off, people pay \( \$ 0.50 \) for each sample bowl of chili. The total cost was \( \$ 6.50 \) for 7 bowls of chili. 3. CJ loves Girl Scout cookies. He eats 3 cookies per hour. After 3 hours, there are 30 cookies left in the box. 4. An oil tank is being filled at a constant rate of 0.2 gallons per minute. After 5 minutes, there are 4 gallons of oil in the tank. 5. The total cost of renting a vacation home includes a deposit and a daily rental fee of \( \$ 125 \). A family rents a vacation home for 3 days and pays \( \$ 450 \). Talk About it! Return to Examples 1-5. Identify the \( y \)-intercept in each scenario. Explain the meaning of the \( y \)-intercept in terms of the context.
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad