Question

solve 2x+3y=5 and mx+ny=m+n​

Answer 1

$\huge\orange{Answer:}$

Solve:

2x+3y=5________(i)

mx+ny=m+n_____(ii)

Multiply (i) by m and (ii) by 2

We get the equation,

$2mx+3my=5m$ _____(iv)

$2mx+2ny=2m+2n$ ___(v)

Subtracting, (iv) and (v)

$2mx+3my-2mx-2ny=5m-2m-2n \\</p><p>=\cancel{2mx}+3my-\cancel{2mx}-2ny=3m-2n\\</p><p> =3my-2ny=3m-2n\\</p><p> =y(3m-2n) =3m-2n\\</p><p> y=\frac{\cancel{3m-2n}}{\cancel{3m-2n}}=1$

Putting, y=1 in 2x+3y=5

$2x+3=5 \\</p><p>2x=2 \\</p><p>x=1$