Determine if the statement is true or false. if a linear system has the same number of equations and variables, then it must have a unique solution. true false justify your answer.

False

Step-by-step explanation:

Consider the equations with the same number of equations and variables as shown below,

Case 1

This equation has no solution because it is not possible to have two numbers that give a sum of 0 and 1 simultaneously.

Case 2

This equation has infinitely many possible solutions.

Therefore it is FALSE to say a linear system with the same number of equations and variables, must have a unique solution.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.