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System of Linear Equations having No Solution
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System of Linear Equations having No Solution

A system of linear equations means two or more linear equations. If these two linear equations intersect, that point of intersection is called the solution to the system of linear equations.
A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied.
Systems have no solution when the lines have same slope (i.e. Lines are parallel) and the lines have different y-intercepts.
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Inequalities in Algebra
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Pythagoras Theorem Example
Characteristic Properties of Similarity
Example: Solve the system of linear equations.
          3x - y = 10
         -6x + 2y = -6
Solution: Given,
          3x - y = 10 ... (i)
        -6x + 2y = -6 ...(ii)
multiplying equation (i) by 2, we get
          6x - 2y = 20 ...(iii)
add the two equations (ii) and (iii)
          0x + 0y = 14 or 0 = 14
As there are no values of x and y for which 0x + 0y = 14, the given system of equations has no solutions. This system is inconsistent.
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