Respuesta :
To solve the question we must know about the System of equations.
System of equation
Inconsistent System
A system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.
The value of k should be 17 so that the system of equations gives infinite number of solutions.
Explanation
Given to us
- 35x + 14y = 119
- 5x +2y = k
As we know that for a system of equations to give an infinite number of solutions. the equations of the system must be either same or in ratio.
In Equation 1
[tex]35x + 14y = 119,[/tex]
dividing both the sides of the equation by 7,
[tex]\dfrac{35x + 14y}{7} = \dfrac{119}{7}\\\\ \dfrac{35x}{7}+\dfrac{14y}{7} = \dfrac{119}{7}\\ 5x+2y = 17[/tex]
As already discussed the system of equations to give infinite number of solutions, the equations must be the same. therefore, comparing both the equations we see that the value of k should be 17.
Hence, the value of k should be 17, so that the system of equations gives infinite number of solutions.
Verification
As we can see in the below image on equating the value of k as 17, the line of the system of equations coincides, therefore, the system will have infinite number of solutions.
Learn more about System of Equations:
https://brainly.com/question/12895249
Answer:
answer is c
Step-by-step explanation:
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