Answer:
(2) 18x - 6y = 42
4x + 6y = 24
Step-by-step explanation:
3x -y =7
2x + 3y = 12
This system has solution x=3; y =2.
And also the system (2). So (2) it's the correct answer.
For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The correct option is B.
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 for the given system of equation is,
3x-y=7
y = 3x - 7
2x+3(3x-7)=12
2x + 9x - 21 = 12
11x = 33
x = 3
y = 2
The system of the equations which satisfies when the value of x=3 and y =2 is substituted will have the same solution as the above system.
A.) 6x -2y = 14
-6x + 9y = 36
18 - 4 = 14
-18 + 18 = 0
B.) 18x - 6y = 42
4x + 6y = 24
54 - 12 = 42
12+12 = 24
Since, both the equation are satisfied this is our solution.
Hence, the correct option is B.
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