Find the point where two straight lines cross, which is the same as solving a system of two linear equations. Drag the points on the graph or type the equations in any form. The answer is exact, and the working is shown step by step by substitution or by elimination.
Drag any of the four points, or tap the grid to move the nearest one there. Or type an equation for each line below.
Where the lines cross
Working
How to use the Intersection Finder
Using the graph
- Line 1 is blue and runs through points A and B. Line 2 is orange and runs through C and D.
- Drag any point, or tap the grid and the nearest point jumps there. The answer updates as you move.
- Snap to sets where points can land. Grid sets how much of the plane you see.
- If the lines cross off the edge of the grid, a box tells you where, with a button to zoom out.
- The example buttons show each kind of pair: crossing, perpendicular, parallel, the same line, and a vertical line.
Typing equations
Type each line in whatever form your question uses. These all work:
- Slope-intercept:
y = 2x - 1,y = -3/4x + 2 - Standard form:
3x + 2y = 6,x - y = 4 - Point-slope:
y - 1 = 3(x - 2) - Vertical and horizontal lines:
x = 4,y = -2 - Anything rearranged:
2y = x + 3,4x = 12 - 3y
Fractions such as 1/2 and decimals such as 0.5 are kept exact.
Reading the answer
- One point: the lines cross once. The answer is that point, written as exact fractions where needed, with a decimal beside it.
- No solution: the lines are parallel. They have the same slope but different y-intercepts, so they never meet.
- Infinitely many solutions: both equations describe the same line, so every point on it is a solution.
- Switch between Substitution and Elimination to see the method your teacher uses. Both give the same answer, and both end with a check in each equation.