Question

Solve the following pair of linear equation by the substitution methods:
8x + 5y = 9
3x + 2y = 4

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Answer 1

SoLuTiOn

8x + 5y = 9 .............(1). × 2

3x + 2y = 4 .............(2). × 5

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16x + 10y = 18 .............(3)

15x + 10y = 20 ............(4)

Subtract equation (3) from (4)

15x + 10y = 20

- 16x + 10y = 18

_______________

- x = 2

X = - 2

On putting x = -2 on equation (4)

15x + 10y = 20

15(-2) + 10y = 20

- 30 + 10y = 20

10y = 20 + 30

$y = \frac{50}{1 0 }$

y = 5

$\therefore \: x = - 2 \\ y = 5$

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Answer 2

Step-by-step explanation:

$8x+5y=9−−−(1)×2 \\ 3x+2y=4−−−(2)×5 \\ 2×1−5×(2) \\ (16x+10y)−(15x+10y)=18−22 \\ x=−2 \\ Putting x=−2 in (2) \\ 3x+2y=4 \\ ⇒3(−2)+2y=4 \\ ⇒2y=10 \\ ⇒y=5 \\ Since point (−2,5) lies on x+y=k \\ So,    −2+5=k \\⇒k=3$