Final answer:
To find the value of λ so that the lines x/2+y/3=1 and x/λ+y/4 intersect at a point, set the equations equal to each other, solve for x and substitute it back into one of the original equations.
Step-by-step explanation:
To find the value of λ so that the lines x/2+y/3=1 and x/λ+y/4 intersect at a point, we can set the equations equal to each other. This gives us x/2+y/3=x/λ+y/4. Now, we can find the value of λ by solving for x in terms of y, and then substituting it back into one of the original equations.
Step 1: Rearrange the equations to solve for x in terms of y:
x = 4λ - 3y
x = 2 + y
Step 2: Set the expressions for x equal to each other:
4λ - 3y = 2 + y
Step 3: Solve for y:
4λ - 4y = 2
-4y = 2 - 4λ
y = (4λ - 2)/4
Step 4: Substitute y back into one of the original equations:
x/2 + ((4λ - 2)/4)/3 = 1
Simplify the equation and solve for λ:
2x + 8λ - 4 = 12
2x + 8λ = 16
8λ = 16 - 2x
λ = (16 - 2x)/8
So, the value of λ is (16 - 2x)/8.