5. Consider the system 2x + z = 3 x+2y+tz= 5 −x + 2y = 4 where t is a real number. It is given to you that the system has a unique solution (x, y, z) with z = 1. Use Cramer's rule to find 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?

Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.

Explain the steps for solving a system of equations using Cramer’s rule.