To solve the question we must know about the System of equations.
<h2>System of equation</h2><h2>Inconsistent System</h2>A system of equations to have no real solution, the lines of the equations must be parallel to each other.
<h2>Consistent System</h2><h3>1. Dependent Consistent System</h3>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.
<h3>2. Independent Consistent System</h3>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.
<h2>Explanation</h2>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.
<h3>In Equation 1</h3>dividing both the sides of the equation by 7,
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.
<h3>Verification</h3>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.
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