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Sum

Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

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#### Solution

We have,

2x + 3y = 11 ….(1)

2x – 4y = – 24 ….(2)

From (1), we have 2x = 11 – 3y

Substituting 2x = 11 – 3y in (2), we get

11 – 3y – 4y = –24

⇒ –7y = – 24 – 11

⇒ –7y = – 35

⇒ y = 5

Putting y = 5 in (1), we get

2x + 3 × 5 = 11

2x = 11 – 15

⇒ x = –4/2 = – 2

Hence, x = – 2 and y = 5

Again putting x = – 2 and y = 5 in y = mx + 3, we get

5x = m(–2) + 3

⇒ –2m = 5 – 3

⇒ m = – 1

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method

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