Question

Find the point of intersection of lines 2x+3y=15 x+4y=6

Answer 1

Answer:

Step-by-step explanation:

Let the two lines are 2x + 3y - 15 = 0 and x + 4y - 6 = 0

If two lines a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0 intersect, then the intersection of the point has coordinates are

x₀ = - c1 b2 + c2 b1 / a1 b2 - a2 b1 and y₀ = - a1 c2 + a2 c1 / a1 b2 - a2 b1

x₀ = - ( - 15 ) 4 + ( - 6 ) 3 / 2 ( 4 ) - 1 ( 3 ) and y₀ = -2 ( - 6 ) + 1 ( - 15 ) / 2 ( 4 ) - 1 ( 3 )

x₀ = 60 - 18 / 8 - 3 and y₀ = 12 - 15 / 8 - 3

x₀ = 42 / 5 and y₀ = - 3 / 5

∴ The point ( x₀ , y₀ ) = ( 42 / 5 , - 3 / 5 ) is the answer.