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 y = 5x + 3 and y = 4x + 6 is (3,18).
What is a System of equations?
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.
The solution of the system of equations can be done as shown below, therefore,
Equation 1: y = 5x + 3
Equation 2: y = 4x + 6
Substitute the value of y from the first equation in the second equation, therefore,
y = 4x + 6
5x + 3 = 4x + 6
5x - 4x = 6 - 3
x = 3
Substitute the value of x in any one of the equation,
y = 5(3) + 3
y = 15 + 3
y = 18
Hence, the solution of the system of equation y = 5x + 3 and y = 4x + 6 is (3,18).
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