Question

How to solve linear equations using graphs

Answer 1

Explanation:

We usually use graphs to solve two linear equations in two unknowns.

The basic idea is that a graph of an equation is the pictorial representation of all of the points that satisfy the equation. So, where the graph of one equation crosses the graph of another, the point where they cross will satisfy both equations.

Finding a solution means finding values of the variables that satisfy all of the equations. Hence, the point of intersection is the solution of the equations.

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To solve linear equations by graphing, graph each of the equations. Then find the coordinates of the point where the lines intersect. Those coordinates are the solution to the equations.

If the solution is not at a grid point on the graph, determining its exact value may not be easy. This can often be aided by a graphing calculator, which can often tell you the point of intersection to calculator accuracy.

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If the lines don't intersect, there are no solutions. If they are the same line (intersect everywhere), then there are an infinite number of solutions.