The value of k for the system of equations such that both lines have infinitely many solutions will be -4/5.
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
A formula known as an equation uses the same sign to denote the equality of two expressions.
Given the system of linear equations,
kx + y = 25
4x − 5y = −125
For the infinity, many solutions,s the ratio of the respective coefficient must be the same.
So,
k/4 = 1/(-5)
k = -4/5
Hence "The value of k for the system of equations such that both lines have infinitely many solutions will be -4/5".
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