Page 97 - Mathematics

Solving linear simultaneous equations

There are several methods of solving Note: Some simultaneous equations
simultaneous equations. This section can be converted into linear
discusses how solutions of linear equations by changing the
simultaneous equations are obtained variables.
by elimination and substitution methods. Tanzania Institute of Education
Example 5.30
Solving linear simultaneous equations
by elimination method Solve the following linear

Elimination method involves performing simultaneous equations by
suitable mathematical operations to elimination method.
reduce the two equations into a single  6x y+= 15
equation with one unknown. The  3x y 9
+=

following are the steps for solving linear
simultaneous equations by elimination Solution
method: Label the equations, say (i) and (ii),
Step 1: Choose the easiest variable to be respectively. That is,
eliminated. Multiply the given
equations by suitable numbers  6x y+= 15 (i)
so as to make the coefficients  3x y 9 (ii)
+=

of the chosen variable in both Choose the easiest variable to be
equations equal. eliminated. In this case, y can be
Step 2: Add the new equations if the eliminated easily.
coefficients of the chosen
variable to be eliminated are Eliminate y to form an equation with
opposite in signs, otherwise variable x only.
subtract them.
Step 3: Solve the obtained equations. The coefficient of y in equation (i)
This gives the value of one of is 1 and in equation (ii) is 1.
the unknowns. Since the signs of the variable y in

Step 4: Repeat steps 1 to 3 for the (i) and (ii) are the same, subtract
value of the second unknown equation (ii) from (i) as follows.
or substitute the solution  6x += 15
y
obtained in step 3 into one of −  3x += 9 Mathematics Form One
y

the equations to get the value 3x = 6
of the other unknown.

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Mathematics form 1.indd 91