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Sum

Solve x + 2y = 10 and 2x + y = 14 by substitution method and hence find the value of m for which y = mx + 8.

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#### Solution

In the given equations,

x + 2y = 10 ......(i)

And 2x + y = 14 ......(ii)

Now, from equation (i), we have

x = 10 – 2y ......(iii)

Substituting the value of x in equation (ii), we get

2(10 – 2y) + y = 14

⇒ 20 – 4y + y = 14

⇒ 20 – 14 = 3y

⇒ 3y = 6

⇒ y = 2

Now, putting the value of y in equation (iii), we get

x = 10 – 2 (ii)

= 10 – 4

= 6

Thus, x = 6 and y = 2

Now, y = mx + 8

⇒ 2 = 6m + 8

⇒ 6m = 2 – 8

⇒ 6m = – 6

m = – 1

As a result, the value of m is – 1.

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

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