Question

If 34x + 43y = –9, 43x + 34y = 9, then x + y is equal to ______.

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Answer 1

If 34x + 43y = –9, 43x + 34y = 9, then x + y is equal to 0.

Explanation:

Given the system of equations:

1. 34x + 43y = –9
2. 43x + 34y = 9

To find x + y:

Multiply equation (1) by 34 and equation (2) by 43: 

(34)(34x + 43y) = 34(–9)

⇒ 1156x + 1462y = –306

(43)(43x + 34y) = 43(9) 

⇒ 1849x + 1462y = 387

Subtract the first from the second:

1849x + 1462y – (1156x + 1462y) = 387 – (–306)

(1849x – 1156x) + (1462y – 1462y) = 693

693x = 693x 

= 1

Substitute x = 1 in equation (1):

34(1) + 43y = –9

34 + 43y = –9

43y = –43y 

= –1

Therefore, x + y = 1 + (–1) = 0.