Question

(1 point) Give a geometric description of the following system of equations 1 2x + 4y - 6z Two parallel planes = " -3- 6y + 9x = 2x + 4y - 62 = Two parallel planes 2. ** –3x - 6y + 9z = 4y - O2 = Two planes intersecting in a line 73. 21 * -x + 5y - 92 = 12 16 –12 18 12 1 T

Answer 1

1.multiply the first equation by 3 and the second equation by 2 ,to see that the cofficients are in the same ratio by the values on the RHS(intercept) differ.so they are parallel.

2.here the coefficients in the LHS and the values on the RHS match after multiplying the first eq. by  -3 and the second eq. by 2.so the planes coincide.(the two equations are same actually).

3.first take z=k and then solve the two simultaneous equations for x and y in terms of k.You get y=(14+24k)/14 and x=(28-3k)/7. So ((28-3k)/7,(14+24k)/14,k) is the solution for the given set of equation ,where k is a real no.

therefore, (7x-28)/3=(14y-14)/24=z/1=k is the equation of the straight line.