Page 102 - Mathematics

Solving linear simultaneous equations by From y + 2x = 11, it implies that,
substitution method y = 11 2x− (iii)

Substitution method involves choosing one Substituting equation (iii) into
equation and transposing one of its variables equation (i) gives,
by making it the subject of the other. The
resulting equation is substituted into the other 3(11 2 ) 2x− − x = − 7
to obtain a single equation with one unknown. Expanding and collecting like terms
The following are the steps for solving gives,
simultaneous equations of two unknowns − 8x = − 40
by substitution method. 40
x =
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Step 1: Express one of the variables in terms 8
of the other from one of the equations. = 5
Substitute x = into equation (iii),
5
Step 2: Substitute the equation obtained in that is,
Step 1 into the second equation to
obtain an equation in one unknown. y = 11− (2 5× )

Step 3: Solve the equation in one unknown = 11 10−
obtained in Step 2. 1=
Therefore, x = 5 and y = 1.
Step 4: Substitute the value of the variable
obtained in Step 3 to one of the
equations to get the value of the other Example 5.36
unknown.
Solve the following simultaneous
Example 5.35 equations by substitution method.

Solve the following simultaneous  6x +  5y = 3
equations by substitution method.  7x + 8y = 10
3y −  2x = − 7 Solution

 y + 2x = 11 Label the two equations:
3
6x +  7x + 8y = 5y = 10 (i)
Solution

Mathematics Form One Using equation (ii), express y in terms of Use equation (i) to express x in
(ii)

Label the two equations as follows.
(i)
7
2x =
−
3y − 
terms of y. That is,

2x =
y +
11
(ii)

3 5y−
x =
(iii)
6
x as follows.
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Mathematics form 1.indd 96 25/10/2024 09:51:33
Mathematics form 1.indd 96