91Ó°ÊÓ

If the three lines are parallel and distinct, it means that they never intersect. In this case, the system would have no solutions. This is because, in order to have a solution, the lines would have to intersect at some point in the plane, but parallel lines do not intersect. In other words, if the three lines are parallel to each other, the slopes of each line are equal. Let's denote the slope of three parallel lines as 'm'. If they are distinct parallel lines, their y-intercepts will be different. Let's represent y-intercepts by b1, b2, and b3. Then, the line equations can be represented as: 1. \(y = mx + b1\) 2. \(y = mx + b2\) 3. \(y = mx + b3\) Since \(b1 \ne b2 \ne b3\), this would lead to an inconsistent system as there are no common points of intersection, and hence we have no solution.

Now, let's consider the case where the three lines are the same, meaning they are essentially the same equation but written in different forms. In this case, the lines have the same slope 'm' and the same y-intercept 'b'. Then, the line equations can be represented as: 1. \(y = mx + b\) 2. \(y = mx + b\) 3. \(y = mx + b\) Here, every point on any of the lines is also on the other two lines, which means that there is an infinite number of solutions since there is an infinite number of points on any line. Conclusion: Based on the two cases discussed, it is true that if the straight lines represented by a system of three linear equations in two variables are parallel to each other, then the system has either no solution or infinitely many solutions.