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Solving a System of Linear Equations by Graphing
To find the solution of a system of two linear equations using a graphical approach, follow this five-step procedure:
- Graph the first equation. Rewrite the equation in a convenient form, such as slope-intercept form, and plot its line on a rectangular coordinate system.
- Graph the second equation on the same coordinate system. Plot the second line on the same grid used for the first equation.
- Determine whether the lines intersect, are parallel, or are the same line. Visually observe the geometric relationship created by the two mapped lines on the graph.
- Identify the solution to the system.
- If the lines intersect, locate the specific point of intersection. The coordinates of this ordered pair represent the single solution to the system.
- If the lines are parallel, they never intersect, meaning the system has no solution.
- If the lines are the same, they perfectly overlap and share every point, meaning the system has an infinite number of solutions.
- Check the solution in both equations. If applicable, substitute the coordinates of the identified point into both original equations to algebraically verify that each equates to a true mathematical statement.
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