Question

Find the value of m and n so that the equations have infinite number of solution 2x+3y=7 m(x+y)-n(x-y)=3m+n-2​

Answer 1

Step-by-step explanation:

given equations are:

$2x + 3y = 7$

$m(x + y) - n(x - y) = 3m + n - 2$

simplify the above equation

$mx + my - nx + ny = 3m + n - 2$

common x and y terms

$(m - n)x + (m + n)y = 3m + n - 2$

Now compare coefficients of two equations.

a1=2, b1=3, c1=7

a2=m-n, b2=m+n, C2= 3m+n-2

for infinite no of solutions

a1/a2= b1/b2= c1/C2

$\frac{2}{m - n} = \frac{3}{m + n} = \frac{7}{3m + n - 2}$

$\frac{2}{m - n} = \frac{3}{m + n}$

$2m + 2n = 3m - 3n$

$m - 5n = 0$

equations

$\frac{3}{m + n} = \frac{7}{3m + n - 2}$

$9m + 3n - 6 = 7m + n$

$2m + 2n = 6$

$m + n = 3$

equation 4

$m - 5n = 0$

$m = 5n$

substitute m value in equation 4

$5n + n = 3$

$n = \frac{1}{2}$

$m = 5 \times \frac{1}{2}$

$m = \frac{5}{2}$