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## SS2: MATHEMATICS - 2ND TERM

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Lesson 8, Topic 1
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# Simultaneous Linear Equations

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#### Topic Content:

• Algebraic Solution
• Substitution Method
• Elimination Method

### Algebraic Solution:

This involves:

1. Substitution Method
2. Elimination Method

### Example 8.1.1:

Use the substitution method to solve the following pairs of simultaneous equations

(a) q + 2r = 8;          r – $$\frac{q}{2}$$ + 1 = 0

(b) y – $$\frac{x}{4}$$ = 3;         3y + x = 23

Solution:

(a) q + 2r = 8;          r – $$\frac{q}{2}$$ + 1 = 0

Simplify $$\scriptsize r \: – \: \normalsize \frac {q}{2} \scriptsize \: + \: 1 = 0$$

Re-write as   $$\scriptsize r\: -\: \normalsize \frac {q}{2} \scriptsize = \: -1$$

Multiply both sides by 2

⇒    2r – q = -2         …………(1)

From the question we write down the other equation

⇒   q + 2r = 8          …………(2)

Make q the subject

⇒     q = 8 – 2r         ………….(3)

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