Find the Points of Intersection of Two Lines

A step by step interactive worksheet solver to find the coordinates of the point of intersection of two lines given by their equations is presented. Unlimited number of practice questions may be generated along with their detailed solutions. Solve each step below then click on "Show me" to check your answer. There is a graph at the bottom of the page that helps you further understand graphically the solution to the question.

Step by step solution


STEP 1: Let the point of intersection of the two lines have coordinates $(a,b)$. Write the system of equations whose solution, if any, is the ordered pair $(a,b)$.




STEP 2: Use Cramers rules to find the determinants $D$, $D_a$ and $D_b$ and solve the system of equations obtained in step (1).




STEP 3: Write the coordinates of the point of intersection.




Graphical Meaning of Solution



Below are shown the graphs of the two lines and the point of intersection if there is any. (Change scales if necessary)


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