Question

Solve x+2y=8 and 2x+y=7​

Answer 1

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$x + 2y = 8 \: \: \: \: \: \: \: \: \: \: \:..........(i)\\ 2x + y = 7 \: \: \: \: \: \: \: \: \: \: \: ..........(ii) \\ \\ adding \: (i)and(ii)..we \: have \: \\ \\ \: x + 2y = 8 \\ \: 2x + y = 7 \\ + \: \: \: + \: \: \: \: = + \\ .................... \\ 3x + 3y = 15 \\ 3(x + y) = 15 \\ x + y = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .....(iii) \\ \\ now \: subtracing \: (i)and(ii)..we \: have \: \\ \\ x + 2y = 8 \\ 2x + y = 7 \\ - \: \: \: - \: \: \: \: = - \\ .................. \\ - x + y = 1 \\ x - y = 1 \: \: \: \: \: \: \: \: .........(iv) \\ x = 1 + y \\ now \: subtituting \: the \: value \\ \: of \: x \: in \: eq \: (iii)..we \: have \\ \\ 1 + y + y = 5 \\ 2y = 5 - 1 \\ y = \frac{4}{2} \\ y = 2 \\ \\ now \: putting \: the \: value \\ \: of \: y \: in \: eq \: (iv) \: ..we \: get \\ x - 2 = 1 \\ x = 3 \\ \\ hence \: the \: value \: of \: x \: and\\ \: y \: is \: 3 \: and \: 2 \: respectively.$

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Answer 2

The given 2 equations are:

x+2y=8 ...................a

and,

2x+y=7​.................b

By the method of cross-multiplication,

multiply the equation a by the  number 2

Which gives,

(x+2y=8) * 2

= 2x+4y=16..................c

Now,

Subtract equation b from c

    2x+4y=16

-    2x+ y=  7​

...............................

      3 y = 9

Solving for y,

3y = 9

y = 9/3

y = 3

Now,

putting the value of y in the equation a

x+2y=8

x + 2 *3 = 8

x + 6 = 8

x = 8 -6

x=2

Hence, the value of x and y are 2 and 3 respectively, which is the solution for equations x+2y=8 and 2x+y=7​

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