ax + by = c....eq. 1 dx + ey = f.....eq 2 gx + hy = k.....eq 3 a) Suppose that t

Question

ax + by = c....eq. 1

dx + ey = f.....eq 2

gx + hy = k.....eq 3

a) Suppose that the originial 3 X 2 has no solution, but the 2 X 2 system using only equations (1) and (2) has infinitely many solutions. Show, geometrically, how this is possible.

b) Suppose that the original 3 X 2 has a unique solution. Then is it possible for the 2 X 2 system using only eq (1) and (2) to have

Infinitly many solutions....yes or no

a unique solution               yes or no

no solution                        yes or no

Explanation / Answer

a) the first two equations are of same line and the third eqn is of a line parallel to them but not same thus, giving infinte soln with first two eqns and no soln with all three

b) for the three lines to have a unique soln the three lines must be concurrent thus, 1st two eqns can either have infinite solns or unique soln

thus, infinitely many solns-yes, unique soln- yes and no soln -no.

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