Question

x+y+z=20 and 5x+2y+0.25z=40 can any one solve this equation

Answer 1

Solving the unsolvable:

The two given equations are

x + y + z = 20

5x + 2y + 0.25z = 40

NOTE: We have two equations with three unknown variables and so the set of equations cannot be solved in a direct method. For this solution, we take random values of either x or y or z, and find the set of solution for other two variables.

We take z = 0. Then the given equations become

x + y = 20

5x + 2y = 40

Multiplying the first equation by 5, we get

5x + 5y = 100

5x + 2y = 40

On subtraction, we get

5x + 5y - 5x - 2y = 100 - 40

or, 3y = 60

or, y = 20

Putting y = 20 in the first equation, we get

x + 20 = 20

or, x = 0

Therefore the required solution is

x = 0, y = 20, z = 0

Geometrical Interpretation: The two linear equations with three variables represent planes in three dimension. When two planes intersect, they make a straight line, and as we know that infinite number of points lie on a straight line, we conclude that there can be infinite number of solutions for the given equations.

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