solve and find the value of k for the following simultaneous equation. 3h-k=2. 2h+k=8
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Step-by-step explanation:
4x+y=7 and 16x+ky=28
Comparing the above equation with the equation a
1
x+b
1
y=c
1
and
a
2
x+b
2
y=c
2
respectively.
a
1
=4,b
1
=1,c
1
=7,
a
2
=16,b
2
=k,c
2
=28
a
2
a
1
=
16
4
=
4
1
,
b
2
b
1
=
k
1
and
c
2
c
1
=
4
1
∴ The condition for the simultaneous equations to have infinitely many solutions is.
a
2
a
1
=
b
2
b
1
=
c
2
c
1
∴
4
1
=
k
1
=
4
1
∴
4
1
=
k
1
∴k=4.
Hence the simultaneous equations 4x+y=7 and 16x+ky=28 will have infinitely many solutions for k=4.
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