Question

$10x + 3y = 75 \\ 6x - 5y = 11$
solve these equations.... ​

Answer 1

Answer:

10x + 3y = 75 ..... (i)

6x -5y = 11 .........(ii)

multiply (i) by 5 and (ii) by 3 then add both the equations..

50x + 15y = 375..

18x - 15y = 33..

68x = 408

x = 6

put x = 6 in any of the equations..

then y = 5

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Answer 2

Given ,

$\to$ 10x + 3y = 75 ----- (i)

$\to$ 6x - 5y = 11 ----- (ii)

$\star$Multiply the eq (i) by 6 and eq (ii) by 10 , we get

$\to$ 60x + 18y = 450 ----- (iii)

$\to$ 60x - 50y = 110 ----- (iv)

$\star$Subtract eq (iv) from eq (iii) , we obtain

$\sf \implies</p><p>60x + 18y - (60x - 50y) = 450 - 110 \\ \\ \sf \implies</p><p>60x + 18y - 60x + 50y = 340 \\ \\ \sf \implies</p><p>68y = 340 \\ \\ \sf \implies</p><p>y = 5$

$\star$Put the value of y = 5 in eq (i) , we obtain

$\sf \implies 10x + 3(5) = 75 \\ \\ \sf \implies</p><p>10x + 15 = 75 \\ \\ \sf \implies</p><p>10x = 60 \\ \\ \sf \implies</p><p>x = 6</p><p>$

Hence , the required values of x and y are 6 and 5