For what value of k does the following pair of linear equations have infinitely many solutions?
10x + 5y – (k – 5) = 0 and 20x + 10y – k = 0.
There are two equations given in the question:
10x + 5y – (k – 5) = 0 …(i)
And, 20x + 10y – k = 0 …(ii)
These given equations are in the form a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 where,
a1 = 10, b1 = 5 and c1 = – (k – 5)
Also, a2 = 20, b2 = 10 and c2 = – k
Now, for the given pair of linear equations having infinite many solutions we must have:
2k – 10 = k
∴ k = 10
Hence, the value of k is 10