An equation with absolute values instead of simple variables has twice as many solutions as an otherwise identical equation with simple variables, because every absolute value has both a negative and a positive counterpart.
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A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
It is essentially a list of equations that have common unknown variables in all of them. For example, a+b-c=3 4a+b+c=1 a-2b-7c=-2 would be a system of equations. If there are the same number of equations and variables you can usually, but not always, find the solutions. Since there are 3 equations and 3 variables (a, b, and c) in this example one can usually find the value of those three variables.
They Are infinitely many solutions for an equation when after solving the equation for a variable(let us suppose x),we get the expression 0 = 0. Or Simply L.H.S = R.H.S For Ex. x+3=3+x x can have any value positive or negative, rational or irrational, it doesn't matter the sequence will be infinite. And No Solutions when after solving the equations the expression obtained is unequal For Ex. x+3=x+5 for every value of x, The Value in L.H.S And R.H.S. will differ. Hence It Has No Solutions.
One equation is simply a multiple of the other. Equivalently, the equations are linearly dependent; or the matrix of coefficients is singular.
Two of them.