6.4.5 Linear Equations, PT3 Focus Practice

Question 15:
Calculate the value of x and of y that satisfy the following simultaneous linear equations:
2x + y = 8
–x + 4y = 5

Solution:
$\begin{array}{l}2x+y=8\mathrm{\dots \dots \dots \dots \dots }\left(1\right)\\ -x+4y=5\mathrm{\dots \dots \dots \dots \dots }\left(2\right)\\ \left(2\right)\times 2:-2x+8y=10\mathrm{\dots \dots \dots ..}\left(3\right)\\ \\ \left(1\right)+\left(3\right):\\ y+8y=8+10\\ 9y=18\\ y=\frac{18}{9}\\ y=2\\ \\ \text{From }\left(1\right):\\ 2x+2=8\\ 2x=8-2\\ 2x=6\\ x=\frac{6}{2}\\ x=3\\ \\ \therefore x=3,y=2\end{array}$

Question 16:
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.