How do you find the solution to a systems of equations graphically?
To find the solution to a system of equations graphically, you need to graph the equations on the same coordinate plane and see where they intersect. This point of intersection represents the values of the variables that satisfy both equations simultaneously.
Here are the steps to graph a system of equations and find the solution graphically:
1. Write the equations in slope-intercept form, y = mx + b.
2. Plot the y-intercept (b) on the y-axis.
3. Use the slope (m) to plot additional points on the line.
4. Connect the points to graph the line.
5. Repeat steps 1-4 for the second equation.
6. Identify the point of intersection, if any, between the two lines.
7. The coordinates of the point of intersection are the solution to the system of equations.
Note: If the two lines are parallel, there is no solution to the system of equations. If the two lines overlap, there are infinitely many solutions.