Question

Problem 1: Solve the systems of equations by the method of your choice.

2x+y=5
x-y=1

Problem 2: 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.

Problem 3: 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.

Problem 4: 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.

Answer 1

x=2 and y=1

Explanation:

2x+y=5

x-y=1

buy adding both equations we get

3x=6

x=2 ( divide 3 on both sides)

put x=2 in any equation

2-y=1

y=2-1

y =1

p2

Problem#2

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°

Problem#3

Total bill = 30

$ 10 Bills = A

$ 20 Bills = B

10 * A + 20* B = 460

A + B = 30

A = 14 , B = 16

Problem#4

4x+2=y

2y−8x=10

The first step is to simplify the second equation into

y=mx+b form.

2y−8x=10y

y−4x=5

y=4x+5

Now, the two equations are:

y=4x+2

y=4x+5