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Simultaneous linear equation in two variables, analytical and graphical solutions. Simultaneous linear in equations. Practical problems on linear equations.

The equations 2x + y = 5 and x + 2y = 4 are

Option:
A. consistent and have a unique solution.
B. consistent and have infinitely many solutions.
C. inconsistent.
D. None of these
Answer: A . consistent and have a unique solution.

Justification:

Equation I:-  2x + y = 5
Equation II:-  x + 2y = 4

.`. We multiply Equation I by 2.
(2x + y = 5) x (2) = (4x + 2y = 10)
We get Equation III = 4x + 2y = 10
Now, We Subtract Equation III & Equation II.
(4x + 2y = 10) - (x + 2y = 4)
.`. (4x - x) + (2y - 2y) = (10 - 4)
.`. (3x) + (0) = (6)
.`. 3x = 6
.`. x = 6/3 = 2
We get x = 2.
Now we add x = 2  in equation II.
Equation II:-  x + 2y = 4
.'. 2 + 2y = 4
.`. 2y = 4 - 2
.`. 2y = 2
.`. y = 2/2
.`. y = 1
Solving given equations, we get : x = 2, y =1.
Thus, (a) is true.

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