Solve if your are 100 % sure. 5. Find the following linear equations. We want to

Question

Solve if your are 100 % sure.

5. Find the following linear equations. We want to solve them by substitution 10-15x+y=0-4) x+2y-1./2) 5.1. Is this problem solvable? 5.2. Solve Eq. (1) for x in terms of y; substitute x in Eq. (2) and solve Eq. (2) for y 5.3. Computers have a certain precision (single precision 10-6 and double precision 1012) so that any numbers smaller than the precision are treated as zero. Redo 5.2 with double precision. 5.4. Redo 5.2 and 5.3, but this time solve Eq.(1) for y in terms of x and solve Eq. (2) for x.

Explanation / Answer

5. The given system of linear equations is 10-15 x +y = 0…(1) and x+2y = 1…(2).

5.1. It is a system of 2 different equations in 2 variables. Therefore, it is solvable.

5.2. As per the 1st equation, we have 10-15 x +y = 0 or, 10-15 x = -y so that x = -1015y. On substituting this value of x in the 2nd equation, we get           -1015y +2y = 1 or, (2-1015)y = 1 so that y = 1/(2-1015). Then x = -1015y = -1015/(2-1015).

5.3 . As per double precision, the given system of linear equations changes to 0*x +y = 0 or, y = 0 and 2y = 1 or, y = 1/2, which is apparently inconsistent.

5.4. As per the 1st equation, we have 10-15 x +y = 0 or, 10-15 x = -y so that y = -10-15 x. On substituting this value of y in the 2nd equation, we get        (1-2*10-15 ) x = 1 so that x =   1/(1-2*10-15 ) = -1015/(2-1015).Then y = -10-15 x = -10-15 [-1015/(2-1015)] = 1/(2-1015).      

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