30. Prove algebraically that the following system intersects at a single point π₁: 2x+y+6z - 7 = 0 π2: 3x+4y+3z + 8 = 0 П3x-2y-4z - 9 = 0

Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.

Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?

Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.