Question

find the value of a and b for which the following pair of linear equations have infinitely many solutions 4x+5y=2 (2a+7b)x+(a+8b)y=2b-a+1

Answer 1

4x+5y=2 


5y = -4x + 2


y = -4/5x + 2/5


(2a+7b)x+(a+8b)y=2b-a+1


(a+8b)y = -(2a+7b)x + (2b-a+1)


y = -(2a+7b)x/(a+8b) + (2b-a+1)/ (a+8b)


For the pair of these linear equations have infinitely many solutions, the coefficients of x (slope) and the constants must be equal


-(2a+7b) /(a+8b) = -4/5 ------ (i)


(2b-a+1)/ (a+8b) = 2/5 ----- (ii)



Solve (i) and (ii) simultaneously


We get a = -1 and b = 2



See the solution below

Answer 2

Answer:

Step-by-step explanation:

Slope of EF = (5-3)/(-2-1)

= -2/3

The slope of the other line is also = -2/3

The other line passes through (2, 6)

Equation of the other line:

y-6 = -2/3(x-2)

y-6 = -2/3x + 4/3

y = -2/3x + 22/3