Pregunta
- OPEN RESPONSE Consider the system of
equations. (Lesson
equations. (Lesson
Ask by Barber Haynes. in the United States
Mar 25,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The system has infinitely many solutions and is dependent.
Solución
-
Write down the system of equations:
-
Substitute the expression for
from the second equation into the first equation: -
Simplify the left-hand side:
-
Combine like terms:
-
Since the equation
is a true statement regardless of the value of , the system has infinitely many solutions. -
Because the two equations describe the same line, the system is dependent.
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Simplifique esta solución Mind Expander
To find the solutions for the given system of equations, we can substitute the second equation into the first. By solving these equations, we find that both represent the same line when simplified, leading to infinite solutions. This makes the system dependent because the equations do not intersect at a single point but rather lie on top of each other.
In terms of graphical representation, if you were to plot both equations on a coordinate plane, you’d see that they perfectly overlap. This visual helps reinforce the concept of dependent systems, indicating that there’s an infinite number of points (solutions) that satisfy both equations at once, rather than just one unique point or none at all.
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