Answer:

m = 5 / 4

C = 37 / 5

Step-by-step explanation:

Given :

A line line passes through intersection of the two lines.

We have given two lines EQUATION. We know it line passes through point it value of x and y satisfy every points.

We have :

x - 23 = - 4 y

Multiply it by 3

- 12 y = 3 x - 69 ... ( i )

7 x = 3 y + 6

Multiply it by 4

12 y + 24 = 28 x

- 12 y = 24 - 28 x .... ( ii )

From ( i )  and ( ii )

3 x - 69 = 24 - 28 x

31 x = 93

x = 3

Putting x = 3 :

x - 23 = - 4 y

- 4 y = - 20

y = 5

Now we have intersection point ( 3 , 5 )

Also the line m y + x = c m passes so it will satisfy value x and y.

5 m + 3 = c m .... ( iii )

Also given :

5 x - 4 y = 6 is PASSING parallel to m y + x = c

Therefore , slope their will be equal :

Slope of the line 5 x - 4 y = 6

Comparing with STANDARD equation :

A x + B y + C = 0

Slope of line m = - A / B

So Slope of the line 5 x - 4 y - 6 = 0

m =  5 / 4

Putting value of m in :

5 m + 3 = c m

25 / 4 + 3 = 5 / 4 c

25 + 12 / 4 =  5 / 4 c

37 = 5 c

c = 37 / 5

Hence the value of m is  5 / 4 and c is 37 / 5 .