The lines x=4y−a and y=4x−b intersect at the point (1,2). What is a+b?
To find the values of a and b, we need to solve the system of equations given by the two lines:
x = 4y - a .......... (1)
y = 4x - b .......... (2)
We are also given that these two lines intersect at the point (1,2), which means that when x = 1 and y = 2, both equations should be true. We can substitute these values into the equations to get a system of equations in terms of a and b:
Using equation (1): 1 = 4(2) - a
Simplifying equation (1): 1 = 8 - a
Rearranging equation (1): a = 8 - 1
a = 7
Using equation (2): 2 = 4(1) - b
Simplifying equation (2): 2 = 4 - b
Rearranging equation (2): b = 4 - 2
b = 2
Therefore, a = 7 and b = 2. To find a + b, we just add these values:
a + b = 7 + 2 = 9
So, the value of a + b is 9.