Question

Determine a and b for which the following system of linear equations has infinite no of solutions 2x-(a-4)=2b+1; 4x-(a-1)y=5b-1.

Answer 1

here,
a₁=2,b₁=4-a,c₁=-(2b-1),a₂=4,b₂=1-a,c₂=1-5b
given equations has infinite solutions
a₁/a₂=b₁/b₂=c₁/c₂
2/4=(4-a)/(1-a)=[-(2b-1)]/[-(5b-1)]

1/2=(4-a)/(1-a)
1-a=8-2a
a=7

1/2=(2b-1)/(5b-1)
4b-2=5b-1
b=-1

Answer 2

a₁=2,b₁=4-a,c₁=-(2b-1),a₂=4,b₂=1-a,c₂=1-5b
given equations has infinite solutions
a₁/a₂=b₁/b₂=c₁/c₂
2/4=(4-a)/(1-a)=[-(2b-1)]/[-(5b-1)]

1/2=(4-a)/(1-a)
1-a=8-2a
a=7

1/2=(2b-1)/(5b-1)
4b-2=5b-1
b=-1