SOLVING LINEAR EQUATIONS IN TWO VARIABLES WORKSHEET

An investor owns shares of Stock A and Stock B. The investor owns a total of 200 shares with a total value of $4000. How many shares of each stock does the investor own?

Stock

Price

$9.50

$27

Solution

Problem 7 :

(a) write an equation that represents the sum of the angle measures of the triangle and (b) use your equation and the equation shown to fi nd the values of x and y

Solution

Answer Key

1) (9, 5).

2) (9, 6).

3) the given pair of linear equations has infinitely many solutions.

4) The error is after deriving for one variable, they have applied the value in the same equation. So, we get no solution.

5) The error is instead of applying the value of x as 6, they have applied the value of y as 6.

6) Number of shares in stock A is 80 and number of shares in stock B is 120.

7) x = 67 and y = 23

Solve the following systems of equations by substitution.

Problem 1 :

0.2x + 0.3y = 1.3

0.4x + 0.5y = 2.3

Solution

Problem 2 :

√2x + √3y = 0

√3x - √8y = 0

Solution

Problem 3 :

(3x/2) - (5y/3) = -2

(x/3) + (y/2) = 13/6

Solution

Problem 4 :

A farmer plants corn and wheat on a 180-acre farm. The farmer wants to plant three times as many acres of corn as wheat. Write a system of linear equations that represents this situation. How many acres of each crop should the farmer plant?

Solution

Problem 5 :

A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. How many of each type of tube does the group rent?

Solution

Example 6 :

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?

Solution

Answer Key

1) (2, 3)

2) (0, 0)

3) (2, 3)

4) the number of acres of wheat is 45 and number of acres of corn is 135.

5) Number of one person tubes is 11 and number of cooler tubes is 4.

6) number of 5 point questions is 8, so number of 2 point questions is 30.

Problem 1 :

Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of "m" for which y = mx + 3.

Solution

Problem 2 :

The difference between two numbers is 26 and one number is three times the other. Find them

Solution

Problem 3 :

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them

Solution

Problem 4 :

You have 40 minutes to exercise at the gym, and you want to burn 300 calories total using both machines. How much time should you spend on each machine?

Solution

Problem 5 :

The sum of the digits of a two-digit number is 11. When the digits are reversed, the number increases by 27. Find the original number.

Solution

Problem 6 :

A radio station plays a total of 272 pop, rock, and hip-hop songs during a day. The number of pop songs is 3 times the number of rock songs. The number of hip-hop songs is 32 more than the number of rock songs. How many of each type of song does the radio station play?

Solution

Answer Key

1) m = -1

2) required two numbers are 39 and 13.

3) two supplementary angles are 99 and 81.

4) You spent 30 minutes in Elliptical trainer and 10 minutes in stationary bike.

5) the required two digit number is 47.

Number of rock songs = 48

Number of pop songs = 144

Number of hip-hop songs = 48 + 32 ==> 80

Problem 1 :

The coach of a cricket team buys 7 bats and 6 balls for $3800. Later, she buys 3 bats and 5 balls for $1750. Find the cost if each bat and each ball.

Solution

Problem 2 :

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is $105 and for a journey of 15 km, the charge paid is $155. What are the fixed charge and charge per km ? How much does a person have to pay for traveling a distance of 25 km ?

Solution

Problem 3 :

The circle graph shows the results of a survey in which 50 students were asked about their favorite meal.

a. Estimate the numbers of students who chose breakfast and lunch.

b. The number of students who chose lunch was 5 more than the number of students who chose breakfast. Write a system of linear equations that represents the numbers of students who chose breakfast and lunch.

c. Explain how you can solve the linear system in part (b) to check your answers in part (a).

Solution

Problem 4 :

A rectangle has a perimeter of 18 inches. A new rectangle is formed by doubling the width w and tripling the lengthℓ, as shown. The new rectangle has a perimeter P of 46 inches.

a. Write and solve a system of linear equations to find the length and width of the original rectangle.

b. Find the length and width of the new rectangle.

Solution

Problem 5 :

The perimeter of the trapezoidal piece of land is 48 kilometers. The perimeter of the rectangular piece of land is 144 kilometers. Write and solve a system of linear equations to find the values of x and y.