The solution to a system of two linear equations is what geometrically?

The solution to a system of two linear equations is what geometrically?

• A. The intersection point of the two lines
• B. The sum of their y-intercepts
• C. The average slope
• D. The product of the slopes

Answer: (A)

Each linear equation in two variables represents a straight line on the plane. The solution set consists of all pairs (x, y) that satisfy both equations, i.e., the points that lie on both lines. Geometrically, that is where the lines intersect. If the lines cross, there is a single intersection point, which is the solution. If they are parallel, there is no common point, so no solution. If they are the same line, infinitely many solutions exist, all along the line. The other options don’t describe where both equations hold true at the same time.

Each linear equation in two variables represents a straight line on the plane. The solution set consists of all pairs (x, y) that satisfy both equations, i.e., the points that lie on both lines. Geometrically, that is where the lines intersect. If the lines cross, there is a single intersection point, which is the solution. If they are parallel, there is no common point, so no solution. If they are the same line, infinitely many solutions exist, all along the line. The other options don’t describe where both equations hold true at the same time.