Acceso
Prima
Hogar Banco de preguntas Matemáticas Álgebra
Pregunta
upstudy study bank question image url

\( 6 x-y-4=0 \) and \( 9 x+1=-2 y \)

Ask by Gray Savage. in South Africa
Feb 20,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

\( x=\frac{1}{3} \) and \( y=-2 \).

Solución

Solve the system of equations \( 6x-y-4=0;9x+1=-2y \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}6x-y-4=0\\9x+1=-2y\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=6x-4\\9x+1=-2y\end{array}\right.\) - step2: Substitute the value of \(y:\) \(9x+1=-2\left(6x-4\right)\) - step3: Expand the expression: \(9x+1=-12x+8\) - step4: Move the expression to the left side: \(9x+12x=8-1\) - step5: Add and subtract: \(21x=8-1\) - step6: Add and subtract: \(21x=7\) - step7: Divide both sides: \(\frac{21x}{21}=\frac{7}{21}\) - step8: Divide the numbers: \(x=\frac{1}{3}\) - step9: Substitute the value of \(x:\) \(y=6\times \frac{1}{3}-4\) - step10: Substitute back: \(y=6\times 3^{-1}-4\) - step11: Calculate: \(y=-2\) - step12: Calculate: \(\left\{ \begin{array}{l}x=\frac{1}{3}\\y=-2\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=\frac{1}{3}\\y=-2\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(\frac{1}{3},-2\right)\) The solution to the system of equations \(6x-y-4=0\) and \(9x+1=-2y\) is \(x=\frac{1}{3}\) and \(y=-2\).

Respondido por UpStudy AI y revisado por un tutor profesional

error msg
Explicar
Simplifique esta solución

The Deep Dive

To solve the equations \( 6x - y - 4 = 0 \) and \( 9x + 1 = -2y \), let's first rearrange them into a more convenient form for solving. The first equation can be rewritten as \( y = 6x - 4 \). For the second equation, rearranging gives \( 2y = -9x - 1 \) or \( y = -\frac{9}{2}x - \frac{1}{2} \). Now we set the right-hand sides equal to each other: \( 6x - 4 = -\frac{9}{2}x - \frac{1}{2} \). Multiplying everything by 2 to eliminate the fraction yields: \( 12x - 8 = -9x - 1 \). Adding \( 9x \) to both sides gives: \( 21x - 8 = -1 \). Adding 8 to both sides results in \( 21x = 7 \), thus \( x = \frac{1}{3} \). Substituting \( x \) back into the first equation to find \( y \): \( y = 6\left(\frac{1}{3}\right) - 4 = 2 - 4 = -2 \). So the solution for the equations is \( x = \frac{1}{3} \) and \( y = -2 \). Enjoy checking the solution by substituting back into both original equations!

preguntas relacionadas

The stopping distance for a car traveling 25 mph is 69.2 feet, and for a car traveling 40 mph it is 112 feet. The stopping distance in feet can be described by the equation \( \mathrm{y}=\mathrm{ax}^{2}+\mathrm{bx} \), where x is the speed in mph. (a) Find the values of a and b . (b) Use the answers from part (a) to find the stopping distance for a car traveling 60 mph . (a) Write the augmented matrix that will be used to find the values of a and b . \( [\square \square 69.2 \) \( \square \) (Type whole numbers.) (Ty
Álgebra United States Feb 22, 2025
An investor plans to put a total of \( \$ 110,000 \) in a money market account, a bond fund, an international stock fund, and a domestic stock fund. She wants \( 60 \% \) of her investment to be conservative (money market and bonds). The investor wants the amount in international stocks to be one-fourth the amount in domestic stocks. Finally, the investor needs an annual return of \( \$ 4,400 \). Assuming the investor gets annual returns of \( 2.5 \% \) on the money market account, \( 3.5 \% \) on the bond fund, \( 4 \% \) on the international stock fund, and \( 6 \% \) on the domestic stock fund, how much should the investor put in each investment? The investor should put \( \$ 8800 \) in the international stock fund. (Type a whole number.) The investor should put \( \$ \square \) in domestic stock fund. (Type a whole number.)
Álgebra United States Feb 22, 2025
An animal breeder can buy four types of food for Vietnamese pot-bellied pigs. Each case of Brand A contains 25 units of fiber, 40 units of protein, and 40 units of fat. Each case of Brand B contains 100 units of fiber, 130 units of protein, and 110 units of fat. Each case of Brand C contains 275 units of fiber, 350 units of protein, and 310 units of fat. Each case of Brand D contains 200 units of fiber, 260 units of protein, and 200 units of fat. How many cases of each brand should the breeder mix together to obtain a food that provides 3975 units of fiber, 5100 units of protein, and 4440 units of fat? Let x represent the number of cases of Brand A, y represent the number of cases of Brand B, z represent the number of cases of Brand C, and w represent be the number of cases of Brand D. There are four ways in which the breeder can mix brands to obtain a food that provides 3975 units of fiber, 5100 units of protein, and 4440 units of fat. If \( w=0 \), the solution is \( (\square, \square, \square, 0) \).
Álgebra United States Feb 22, 2025
\( \left. \begin{array} { l } { 102 ^ { x } - 2 ^ { y + 2 } = 0 } \\ { x ^ { 2 } + 2 x y + y ^ { 2 } = 36 } \end{array} \right. \)
Álgebra South Africa Feb 22, 2025
An animal breeder can buy four types of food for Vietnamese pot-bellied pigs. Each case of Brand A contains 25 units of fiber, 40 units of protein, and 40 units of fat. Each case of Brand B contains 100 units of fiber, 130 units of protein, and 110 units of fat. Each case of Brand C contains 275 units of fiber, 350 units of protein, and 310 units of fat. Each case of Brand D contains 200 units of fiber, 260 units of protein, and 200 units of fat. How many cases of each brand should the breeder mix together to obtain a food that provides 3975 units of fiber, 5100 units of protein, and 4440 units of fat? Let \( x \) represent the number of cases of Brand A, y represent the number of cases of Brand B, z represent the number of cases of Brand C, and w represent be the number of cases of Brand \( D \). There are four ways in which the breeder can mix brands to obtain a food that provides 3975 units of fiber, 5100 units of protein, and 4440 units of fat. If \( w=0 \), the solution is \( (0,15,9,0) \). If \( w=1 \), the solution is \( (\square, \square, \square, 1) \).
Álgebra United States Feb 22, 2025

Latest Algebra Questions

The stopping distance for a car traveling 25 mph is 69.2 feet, and for a car traveling 40 mph it is 112 feet. The stopping distance in feet can be described by the equation \( \mathrm{y}=\mathrm{ax} 2+\mathrm{bx} \), where \( x \) is the speed in mph. (a) Find the values of a and b . (b) Use the answers from part (a) to find the stopping distance for a car traveling 60 mph . \( \left[\begin{array}{ll|l}625 & 25 & 69.2 \\ 1600 & 40 & 112\end{array}\right] \) (Type whole numbers.) The value of a is \( \square \). The value of b is \( \square \). (TvDe inteaers or decimals rounded to six decimal places as needed.)
Álgebra United States Feb 22, 2025
The stopping distance for a car traveling 25 mph is 69.2 feet, and for a car traveling 40 mph it is 112 feet. The stopping distance in feet can be described by the equation \( \mathrm{y}=\mathrm{ax}^{2}+\mathrm{bx} \), where x is the speed in mph. (a) Find the values of a and b . (b) Use the answers from part (a) to find the stopping distance for a car traveling 60 mph . (a) Write the augmented matrix that will be used to find the values of a and b . \( [\square \square 69.2 \) \( \square \) (Type whole numbers.) (Ty
Álgebra United States Feb 22, 2025
Solve for \( w \) \[ -39=2(w+3)+3 w \] Simplify your answer as much as possible.
Álgebra United States Feb 22, 2025
\( \left. \begin{array} { l } { 102 ^ { x } - 2 ^ { y + 2 } = 0 } \\ { x ^ { 2 } + 2 x y + y ^ { 2 } = 36 } \end{array} \right. \)
Álgebra South Africa Feb 22, 2025
An animal breeder can buy four types of food for Vietnamese pot-bellied pigs. Each case of Brand A contains 25 units of fiber, 40 units of protein, and 40 units of fat. Each case of Brand B contains 100 units of fiber, 130 units of protein, and 110 units of fat. Each case of Brand C contains 275 units of fiber, 350 units of protein, and 310 units of fat. Each case of Brand D contains 200 units of fiber, 260 units of protein, and 200 units of fat. How many cases of each brand should the breeder mix together to obtain a food that provides 3975 units of fiber, 5100 units of protein, and 4440 units of fat? cases of Brand D. There are four ways in which the breeder can mix brands to obtain a food that provides 3975 units of fiber, 5100 units of protein, and 4440 units of fat. If \( w=0 \), the solution is \( (0,15,9,0) \). If \( w=1 \), the solution is \( (1,10,10,1) \). If \( w=2 \), the solution is \( (2,5,11,2) \). If \( w=3 \), the solution is \( (\square, \square, \square, 3) \).
Álgebra United States Feb 22, 2025
Anterior Próximo
¡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