Question

Solve 23x-29y=98 and 29x-23y=110

Answer 1

Hey dear friend here's ur answer :-)

23x − 29y = 98    ....(1)

29x − 23y = 110     ...(2)

Adding (1) and (2), we get

52x − 52y = 208

52 (x-y) =208

⇒x − y = 4     .....(3)

Subtracting (2) from (1), we get

−6x − 6y = −12
⇒x + y = 2      ....(4)
adding (3) and (4), we get
2x = 6
⇒x = 3
Now, from (4), we get
y = −1

Hence, x=3 and y= -1..

hope it helps :-)

#thank you

Answer 2

Given equations are

$23x - 29y = 98 \\ 29x - 23y = 110$

The easy way to solve these kind of problems is to add these equations to get a new equation 1, and subtract these equations to get a new equation 2.

Adding the above equations we get

$23x - 29y + 29x - 23y = 98 + 110 \\ 52x - 52y = 208 \\ 52(x - y) = 52 \times 4 \\ x - y = 4$

Now subtracting these two equations we get

$23x - 29y - 29x + 23y = 98 - 110 \\ - 6x - 6y = - 12 \\ - 6(x + y) = - 6 \times 2 \\ x + y = 2$

We got two new equations which are simpler to solve. Now adding the two new equations we get

$x - y + x + y = 4 + 2 \\ 2x = 6 \\ x = 3$

Now substitute the value of x in any of the new equations

$x - y = 4 \\ 3 - y = 4 \\ y = - 1$

Therefore the values of x and y are

$x = 4 \\ y = - 1$

#SPJ2