LINEAR and SIMULTANEOUS EQUATIONS

 1. Linear equations

   QUESTION 1. 

   QUESTION 2.

  QUESTION 3.

  QUESTION 4.

QUESTION 5.

 QUESTION 6.

QUESTION 7.

QUESTION 8.

SOLUTION

This problem involves setting up and solving a system of linear equations to compare two different services.

Traveling 50 km is cheaper with Company B because its lower flat fee outweighs the higher per-kilometre rate at this relatively short distance.

Di chuyển 50 km sẽ rẻ hơn với Công ty B vì phí cố định thấp hơn của họ bù đắp cho mức phí trên mỗi km cao hơn ở khoảng cách tương đối ngắn này.

QUESTION 9.

QUESTION 10.

       Use rectangle ABCD and the given information to complete the following.

    (a)  If 𝐴𝐶 = 4𝑥 − 60 and 𝐵𝐷 = 30 − 𝑥, find 𝐵D. 

    (b)  If ∠𝐵𝐴𝐶 = 4𝑥 + 5 and ∠𝐶𝐴𝐷 = 5𝑥 − 14, find ∠𝐶𝐴𝐷.

    (c)  If 𝐷𝐸 = 13, find 𝐶𝐸.

QUESTION 11.
        Use square ABCD and the given information to complete the following.

     (a) If 𝐵𝐶 = 3𝑥 + 14 and 𝐷𝐶 = 5𝑥 − 8, find the value of 𝑥.

     (b) If ∠𝐴𝐸𝐵 = 3𝑥, find the value of 𝑥.

     (c) If ∠𝐵𝐴𝐶 = 5𝑥, find the value of 𝑥.

QUESTION 12.

     ABCD is an isosceles trapezoid with bases 𝐴𝐵 and 𝐶𝐷, and median 𝐸𝐹. Use the given information to solve each problem. 

     (a)  If 𝐷𝐶 = 30 and 𝐴𝐵 = 42, find 𝐸𝐹.

     (b)  If ∠𝐴 = 5𝑥 and ∠𝐷 = 4𝑥, find the value of 𝑥.

     (c)  If 𝐸𝐹 = 𝑥 + 5 and 𝐴𝐵 + 𝐶𝐷 = 4𝑥 + 6, find 𝐸𝐹.

QUESTION 13.

QUESTION 14.

     A shape  is made from 4 congruent  parallelograms and a rhombus. The area of the shape is 792cm².  Find the value of y . 

QUESTION 15.

QUESTION 16.

QUESTION 17.