Let us subtract equation 1 from equation 2.
5x - 3y - 2x + 3y = 7 - 4
3x = 3
x = 1
Substituting this value of x in equation 1, we get
2x - 3y = 4
2 - 3y = 4
-3y = 2
y = [tex]\frac{-2}{3}[/tex]
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 will be at (1, -2/3).
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.
Use can solve the given system of equations using the combination method as shown below.
1. Subtract the first equation from the second equation.
5x - Зу - (2x - 3y) = 7 - 4
5x - 3y -2x + 3y = 3
3x = 3
x = 1
2. Substitute the value of x in any one of the equation.
5x - 3y = 7
5(1) - 3y = 7
5 - 3y = 7
-3y = 7 - 5
y = -(2/3)
Hence, the solution of the system of equation will be at (1, -2/3).
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