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Mkey [24]
3 years ago
12

Given that 3x+2y=5a+b and 4x-3y=a+7b, solve for y-x in terms of a and b.​

Mathematics
1 answer:
Eduardwww [97]3 years ago
3 0

Answer:

y - x = - 2 b

Step-by-step explanation:

Given-

3 x + 2 y = 5 a + b...................(i)

4 x - 3 y = a + 7 b.....................(ii)

<em><u>Multiply by 3 and 2 in equation (i) & (ii) respectively-</u></em>

<em><u>Add equation (iii) &  (iv)-</u></em>

9 x + 6 y = 15 a + 3 a...................(iii)

<u>8 x - 6 y = 2 a + 14 b</u> ...................(iv)

17 x = 17 a + 17 b

<u>x = a + b</u>

Put x = a + b in equation (i)-

<em>2 y = 5 a + b - 3 a - 3 b</em>

<em>2 y = 2 a - 2 b</em>

<u>y = a - b </u>

<em>∴ y - x = a - b - ( a + b )</em>

<em>y - x = a - b - a - b</em>

y - x = - 2 b

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