For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The solution of the system of equation is (-3.4, -9).
Inconsistent System
For 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
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
Add the two equations,
–2.1x + 4y + 2.1x – 5.5y = –0.2 + 5.3
-2.1x + 2.1x + 4y -5.5y = 5.1
-1.5 y = 5.1
y = 5.1/1.5
y = -3.4
Now, substitute the value of y in any one of the equation, therefore,
-2.1x + 4y = 5.3
-2.1x + 4(-3.4) = 5.3
-2.1x - 17.36 = 5.3
-2.1x = 22.66
x = -9
Hence, the solution of the system of equation is (-3.4, -9).
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