6.5.2 Linear Equations, PT3 Focus Practice


Question 5:
It is given that + 2y = 4 and x + 6y = –4.
Calculate the value of x.

Solution:
Using Elimination method
+ 2y = 4 ——– (1)
+ 6y = –4 ——- (2)
(1) × 3:  3x + 6y = 12 ——– (3)
   x + 6y = –4 ——- (2)
(3) – (2): 2= 12 – (–4)
2x = 16
  x = 8



Question 6:
Calculate the value of x and of y that satisfy the following simultaneous linear equations:
2x + y = 8
x + 4y = 5

Solution:
2x+y=8 …………… ( 1 ) x+4y=5  …………… ( 2 ) ( 2 )×2:   2x+8y=10  ……….. ( 3 ) ( 1 )+( 3 ):   y+8y=8+10 9y=18 y= 18 9 y=2 From ( 1 ): 2x+2=8 2x=82 2x=6 x= 6 2 x=3 x=3, y=2

Question 7:
Diagram below shows 5 boxes of orange juice and 2 bottles of milk. Both orange juice and milk are mixed to produce 18 litres drink.


(a) Based on the above situation, write a linear equation.
(b) If 9 litres of drinks is produced by using 2 boxes of orange juice and 2 bottles of milk, find the volume, in litre, of orange juice in each box.

Solution:
Let j be the number of boxes of orange juice and m be the number of bottles of milk.
(a)
5j + 2m = 18

(b)
2j+2m=9  …………. ( 1 ) 5j+2m=18 …………. ( 2 ) ( 2 )( 1 ): 3j=9 j= 9 3 =3 3 litres of orange juice in each box.


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