Explain why the solutions of the simultaneous equations ax+by+c=0 dx+ey+f=0 have rational expression in {a,b,c,d,e,f}...



Answered question


Explain why the solutions of the simultaneous equations
ax+by+c=0 dx+ey+f=0
have rational expression in {a,b,c,d,e,f} whenever aebd.

Answer & Explanation

Bertha Stark

Bertha Stark

Skilled2021-09-23Added 96 answers

Step 1
given simultaneous equations are,
ax+by+c=0 and
Step 2
given system can be written as,
ax+by=c and
above system is non homogeneous system of equation,
compaire it with ax=b
when ae=bd then we get a solution in integer.
and if aebd then we have to solve system of simultaneous equation by using row transformation.
R2=R2dR1 gives,
by solving x and y we get rational expressions,
so we have a rational expressions in {a,b,c,d,e,f} whenever aebd.

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