Question

Which value of k would cause the system of linear equations 35 x 14 y = 119 and 5 x 2 y = k to have an infinite number of solutions? 3 7 17 21.

Answer 1

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

$35x + 14y = 119,$

dividing both the sides of the equation by 7,

$\dfrac{35x + 14y}{7} = \dfrac{119}{7}\\\\ \dfrac{35x}{7}+\dfrac{14y}{7} = \dfrac{119}{7}\\ 5x+2y = 17$

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:

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