To find the intersection point of two lines, enter the slope (m) and y-intercept (b) for both equations into the input fields. This tool uses the Substitution Method, which is the most efficient way to solve systems where both equations are already solved for Y. It works perfectly with integers, negative numbers, and decimal values.
When you click “Solve System,” the whiteboard logic triggers. It sets the two expressions equal to one another, effectively eliminating the Y variable so you can solve for X. The tool uses Smart Aligning to show subtraction and division steps directly beneath the corresponding terms, ensuring the math is easy to follow visually.
Our solver is designed to catch special geometric cases automatically. If the slopes of the two lines are identical but the intercepts differ, the tool identifies them as Parallel Lines and informs you there is no solution. If both the slope and intercept match, it recognizes the equations as the Same Line, indicating infinite solutions.
After finding the value of X, the tool performs a “back-substitution” by plugging that value into the first equation to determine the Y-coordinate. The final result is presented as a clean (x, y) coordinate pair. You can toggle the “Show Steps” feature off if you only want the final answer, or keep it on to verify every detail of the calculation.
System of Equations: This is just a fancy way of saying “two or more equations that work together.” We look at them at the same time to see where they agree.
Intersection Point: This is the exact spot on a graph where two lines cross each other. It is written as (x, y). At this specific point, both equations are true at the same time.
Substitution: This means “replacing.” Since both lines equal y, we replace the y in one equation with the math from the other equation. This helps us get rid of one variable so we can solve the problem.
Parallel Lines: These are lines that have the exact same steepness (slope) but start at different heights. Because they stay the same distance apart forever, they will never cross, which means there is no solution.
Coefficient: This is just the number sitting right next to the x. It tells us how much to multiply x by. If you see just x by itself, the coefficient is hidden—it is actually a 1.