1) The difference of two complementary angles is 30 degrees. Set up a system of linear equations that would find the angles. Do not solve the system.
2) A cashier has 30 bills, all of which are $10 or $20 bills. The total value of the money is $460. Set up a system of linear equations that would find how many of each type of bills the cashier has. Do not solve the system.
3) Give an example of a system of linear equations that has no solutions. Explain how can you decide the number of solutions without solving the system.
Answers
Given : The difference of two complementary angles is 30 degrees
To Find : . Set up a system of linear equations that would find the angles.
Solution:
Let say two complementary angles are A & B
difference of two complementary angles is 30°
=> A - B = 30
Sum of two complementary angles is 90°
=> A + B = 90
Hence A = 60° , B = 30°
Total bill = 30
$ 10 Bills = A
$ 20 Bills = B
10 * A + 20* B = 460
A + B = 30
A = 14 , B = 16
x + y = 2
x + y = 3
Has no solution
a₁x + b₁y = c₁
a₂x + b₂y = c₂
Consistent if
a₁/a₂ = b₁/b₂ = c₁/c₂ ( Infinite solution , same line )
or a₁/a₂ ≠ b₁/b₂ ( unique solution , intersecting lines )
Inconsistent if
a₁/a₂ = b₁/b₂≠ c₁/c₂ ( no solution , Parallel lines)
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