If the line my+x=cm passes through the point of intersection of the lines x-23=-4y and 7x=3y+6 and parallel to the line 5x-4y=6 ,then find the value of m and c.
Answers
Answer:
m = -4/5 and c = 5/4
Step-by-step explanation:
For point of intersection: when x - 23 = -4y and 7x=3y+6 meet is the point when both x(s) are and both y(s) are same. Solving both:
Multiply x - 23 = - 4y by 7 and subtract from the 2nd equation.
7x = 3y + 6
- 7x = + 28y - 161
0 = 31y - 155 ⇒ y = 5
Thus,
x - 23 = -4y ⇒ x = -4(5)+23 ⇒ x = 3
Point of intersection is (x , y) = (3, 5)
As it is || to 5x - 4y = 6, slope must of both must be same.
On comparing with y = m₁x + c, we get slope = m₁ = 5/4 , m₁ is slope* and not that which is given in question.
Hence, equation of the lines is:
⇒ y - y₁ = m₁(x - x₁)
⇒ y - 5 = (5/4)(x - 3)
⇒ -4y+ 5x = - 5 [divide by 5]
⇒ -(4/5) y + x = - 1
Compare with my + x = cm :
my = -(4/5)y ⇒ m = -4/5
∴ cm = -1 ⇒ c(-4/5) = -1 ⇒ c=5/4