Explain the difference between solving a linear equation graphically and solving a system of equations graphically.

How would I go about doing this?

when you solve a linear equation you mean find y for a given x, or find x for a given y, just one point if the lines are not parallel or the same.

when you solve a system, you find the points where the lines cross.

To understand the difference between solving a linear equation graphically and solving a system of equations graphically, let's first define these terms:

1. Solving a linear equation graphically: This involves finding the value(s) of the variable that make the equation true by representing the equation on a graph and identifying the point(s) where the graph intersects the x-axis.

2. Solving a system of equations graphically: This refers to finding the values of the variables that simultaneously satisfy multiple equations in a system by representing each equation graphically and identifying the point(s) where the graphs intersect.

Now, let's discuss the process for solving each:

1. Solving a linear equation graphically:
- Plot the equation on a graph by creating a coordinate system.
- Convert the equation into slope-intercept form, y = mx + b, if it's not already in that form.
- Identify the y-intercept (b) and plot the point (0, b) on the graph.
- Use the slope (m) to find a second point. For example, if the slope is 2/3, move 2 units up and 3 units to the right (or down/left if the slope is negative) from the y-intercept to find the second point.
- Draw a straight line passing through these two points.
- Identify the x-intercept(s) by finding the point(s) where the line crosses the x-axis. These x-values are the solutions to the equation.

2. Solving a system of equations graphically:
- Plot each equation on the same graph by creating a coordinate system.
- Convert the equations into slope-intercept form, y = mx + b, if they are not already in that form.
- Identify the y-intercept (b) for each equation and plot the points (0, b) on the graph for each equation.
- Use the slopes (m) to find second points for each equation.
- Draw a straight line passing through the two points for each equation.
- Identify the point(s) of intersection between the lines on the graph. These intersection point(s) represent the values of the variables that satisfy all the equations simultaneously and are the solutions to the system of equations.

In summary, the key difference between solving a linear equation graphically and solving a system of equations graphically is that a linear equation has only one unknown variable, while a system of equations has multiple unknown variables. As a result, solving a linear equation graphically involves finding the x-intercept(s) of the equation on the graph, while solving a system of equations graphically involves finding the point(s) of intersection between the graphs of the equations.