Question

22s = -11t + 16 ;
44(t + 2s) = 12
Consider the system of equations above. How many solutions (s, t) does this system have ?

• A. Exactly 1
• B. Exactly 2
• C. Infinitely Many

Answer 1

Write the equations in the standard form :
22s + 11t = 16
88s + 44t = 12
Ratios of coefficient s : $\frac{22}{88}=\frac{1}{4}$
Ratio of coefficient t : $\frac{11}{44}=\frac{1}{4}$
Ratio of constant : $\frac{16}{12}=\frac{4}{3}$
As Ratios of coefficient s = Ratio of coefficient $t\ne$ Ratio of constant
Therefore the system describes lines which are parallel and does not have any solution.
Hence, option A is correct.