Question

EXERCISE 8.4
1. The sum of two numbers is 70. Their difference is 16. Find the numbers.(linear equations)
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Answer 1

Let the number be x and y

As ᴍᴇɴᴛɪᴏɴᴇᴅ ɪɴ ᴛʜᴇ Qᴜᴇsᴛɪᴏɴ,

x + y = 70

x - y = 16

Using the method of elimination, eliminating y.

Adding both the equations,

$x \: \cancel{+ y} = 70$

+($\sf x \: \cancel{ - y }= 16$)

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2x = 86

$\bf x = \cancel{ \dfrac{86}{2}} = 43$

$\boxed{\bf x = 43}$

Substituting the value of x in any 2nd eq,

→ x - y = 16

→ 43 - y = 16

→ y = 43 - 16

→ $\boxed{\bf y = 27}$

________________

Therefore, the numbers are 27 and 43.

★ᴠᴇʀɪғɪᴄᴀᴛɪᴏɴ:-

Sum of both the numbers 27 + 43 = 70

Difference = 43-27 = 16

Hence, Verified ✅

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