How to Find Where Two Lines Intersect

The Organic Chemistry Tutor

This instructional video provides a step-by-step tutorial on solving a system of two linear equations to find their point of intersection. The narrator introduces a specific problem involving one equation in slope-intercept form and another in standard form. He demonstrates two distinct methods to solve the problem: an algebraic approach using substitution and a geometric approach using graphing on a coordinate plane. The video covers key algebraic concepts including substituting variables, distributing negative numbers, combining like terms, and isolating variables to solve for x and y. It also details the process of converting an equation from standard form to slope-intercept form to facilitate graphing. The graphing section visually reinforces the algebraic solution by plotting y-intercepts and using slope triangles to find the exact coordinate where the two lines cross. This resource is highly valuable for Algebra students as it connects abstract algebraic manipulation with concrete visual representations. By showing two methods side-by-side, it helps students understand that a "system solution" is literally the point where two graphs meet. It is an excellent tool for introducing systems of equations, reviewing graphing skills, or demonstrating how to verify mathematical answers using multiple strategies.