How to Algebraically Find the Intersection of Two Lines

To algebraically find the intersection of two lines, you need to follow these steps:

Step 1: Write the equations of the two lines in slope-intercept form. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

For example, let's say we have two lines: - Line 1: y = 2x + 1 - Line 2: y = -3x + 5

Step 2: Set the two equations equal to each other and solve for x. This will give you the x-coordinate of the intersection point.

2x + 1 = -3x + 5 5x = 4 x = 4/5

Step 3: Substitute the x-coordinate into one of the original equations and solve for y. This will give you the y-coordinate of the intersection point.

Using Line 1: y = 2(4/5) + 1 y = 9/5

Therefore, the intersection point of the two lines is (4/5, 9/5).

Note: If the two lines are parallel, they will never intersect and there will be no solution. If the two lines are the same, they will intersect at every point on the line and there will be infinitely many solutions.