Question

Solve by elimination method 11x + 10y = 21 and 14x + 21y = 41

Answer 1

Step-by-step explanation:

11x+10y=21......(1)

14x+21y=41......(2)

multiplying (1) by 21 and (2) by 10 and subtracting (2) from (1)

231x+210y=441

140x+210y=410

__ __ __

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91x=31

x=31/91

putting value of x in (1)

11x+10y=21

11*31/91+10y=21

10y=21-341/91

10y= 1911-341/91

y=1570/910

y=157/91

Answer 2

Solution :-

We are provided with

11x + 10y = 21 ....(i)

14x + 21y = 41 ....(ii)

Question asks it to solve via elimination method .

We will multiply the first equation by 21 and second by 10

So (i) × 21

= 231x + 210y = 441 ....(iii)

So (ii) × 10

= 140x + 210y = 410 .....(iv)

Now we will subtract equation (iv) from (iii)

231x + 210y = 441

- 140x - 210y = - 410

____________________

91x + 0y = 31

→ 91x = 31

$\rightarrow x = \dfrac{31}{91}$

Now by putting the value of x in equation (i)

$\rigtarrow 11x + 10y = 21$

$\rightarrow 11 \times \dfrac{31}{91} + 10y = 21$

$\rightarrow \dfrac{341}{91} + 10y = 21$

$\rightarrow 10y = 21 - \dfrac{341}{91}$

$\rightarrow 10y = \dfrac{1911 - 341}{91}$

$\rightarrow y = \dfrac{1570}{910}$

$\rightarrow y = \dfrac{157}{91}$

So

$\rightarrow x = \dfrac{31}{91}$

$\rightarrow y = \dfrac{157}{91}$