Writing Describe how to determine the solution of a system of two linear equations by graphing.
To determine the solution of a system of two linear equations by graphing, follow these steps:
1. Begin by writing down the given equations in standard form, which is Ax + By = C. Make sure that both equations are written in this form.
2. Choose suitable values for x and solve the equation to find corresponding values for y. Repeat this process for both equations to obtain two sets of x and y values.
3. Plot these points on a graph. Remember to label the x and y axes accordingly.
4. Connect the two points for each equation on the graph using a straight line. Make sure that the lines are represented accurately and extend them beyond the given points if needed.
5. Analyze the graph to determine the point of intersection of the two lines. This point represents the solution to the system of equations.
6. If the lines intersect at a single point, then that point is the solution. The x and y coordinates of this point represent the values that satisfy both equations simultaneously.
7. If the lines are parallel and do not intersect, then there is no solution to the system of equations. This means the two equations are inconsistent and have no common solution.
8. If the lines coincide or overlap, then there are infinitely many solutions to the system of equations. This occurs when the two equations are equivalent.
Remember to double-check your work and ensure that your graph accurately represents the given equations.
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To determine the solution of a system of two linear equations by graphing:
1. Write the equations in the form Ax + By = C.
2. Choose values for x and solve to find corresponding y values for each equation.
3. Plot the points on a graph.
4. Connect the points with straight lines.
5. The intersection point of the lines is the solution.
6. If the lines are parallel, there is no solution.
7. If the lines overlap, there are infinitely many solutions.