Question

PROBLEM 1 Find coefficients b and g such that the lines defined by the equations 2r by 16, a) Don't intersect. b) Intersect at at least two points. PROBLEM 2 Which number q makes this system singular and which right side t gives it infinitely many solutions? Find the solution that has 1.

Answer 1

Given 2x + by = 16 4x + 8y = g two straight line don't inter set only when both lines are parallel. ie slope of both lines are equal m_1 = m_2 - b/2 = -8/4 Therefore b = 4 {A alpha + BY = C m = -B/A} \r\n It is possible that two straight line consider then it will be more that two no inter section point So, A_1/A_2 = B_1/B_2 = C_1/C_2 = K implies 2/4 = b/8 = 16/g implies b = 4 g = 32 So, for Here two line do not inter set g should not be equal to 32 ie g notequalto 32 \r\n Two lines inter set at least two point only when Here two line consider, Therefore 2/4 = b/8 = 16/g (A_1/A_2 = B_1/B_2 = C_1/C_2 = K) 2/4 = B/8, 2/4 = 16/g Therefore b = 4 g = 32 when b = 4 and g