Answer :
Answer:
x=1,y=-2
Step-by-step explanation:
To find the values of k and p for the point (1, p), we start by substituting x = 1 and y = p into the equations provided:
y = kx - 5 Substitute x = 1: y = k(1) - 5 y = k - 5
4x^2 - xy = 6 Substitute x = 1 and y = p: 4(1)^2 - (1)(p) = 6 4 - p = 6 p = 4 - 6 p = -2
By comparing the first equation with the second equation, we get: k - 5 = -2 k = -2 + 5 k = 3
Therefore, the values for k and p for the point (1, p) are k = 3 and p = -2.
To find the second pair of solutions for the system of equations, we can solve the equations simultaneously:
y = kx - 5
4x^2 - xy = 6
Substitute the expression for y from equation 1 into equation 2: 4x^2 - (kx - 5)x = 6 4x^2 - kx^2 + 5x = 6 Factor out x: x(4 - k) + 5 = 6
Now, since (1, p) is a solution, substitute x = 1 and y = p into equation 1: p = 3*1 - 5 p = -2
Therefore, the second pair of solutions for the system of equations are x = 1 and y = -2.