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 = 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 .
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