Question

Find the value of m and n so that tha function . = + −x a solution of Given differential equations ′′ − ′ − = 0 () = , ′() = 2

Answer 1

Question:

Determine the value of m and n so that the following system of linear equation have an infinite number of solutions.

$(2m-1)x+3y-5=0$

and

$3x+(n-1)y-2=0$

Answer:

$m=\frac{17}{4}$

$n = \frac{11}{5}$

Step-by-step explanation:

Given

$3x+(n-1)y-2=0$

$(2m-1)x+3y-5=0$

Rewrite both equations:

$3x + (n - 1)y = 2$

$(2m - 1)x + 3y = 5$

For the expression to have a solution, the following condition must exist:

$\frac{3x}{(2m - 1)x} = \frac{(n-1)y}{3y}= \frac{2}{5}$

Split to 2

$\frac{3x}{(2m - 1)x} = \frac{2}{5}$

$\frac{(n-1)y}{3y}= \frac{2}{5}$

Cross Multiply

$5 * 3x = 2 * (2m - 1)x$ -- (1)

$5 * (n -1)y = 2 * 3y$ -- (2)

Solving (1)

$5 * 3x = 2 * (2m - 1)x$

Divide both sides by x

$5 * 3 = 2 * (2m - 1)$

Open bracket

$15 = 4m - 2$

Collect Like Terms

$4m = 15+2$

$4m= 17$

Make m the subject

$m=\frac{17}{4}$

Solving (2)

$5 * (n -1)y = 2 * 3y$

Divide both sides by 7

$5 * (n - 1) = 2 * 3$

Open bracket

$5n - 5 = 6$

Collect Like Terms

$5n = 5 + 6$

$5n = 11$

Make n the subject

$n = \frac{11}{5}$