I need help with this problem because I do not have a graphing calculator.

Explain how you would solve this equation using your graphing calculator in five steps then give the solution.
2x- 3y=8
5x+ 4y= 11

Also how do you determine how many solutions a system of equations has without solving the system?

There are three possible solutions for system of equation.

1. zero, same slope different y intercept (two lines are parallel)
2. one, which means the two lines intersect once ( different slope & y- intercept )
3. infinite, which means the two line have the same slope and y-intercept.

you don't have to solve the system of equation but you have to get y by itself so that you know what the slope and y-intercept are.

2x-3y=8 ---> y=-2/3x-8/3
5x+4y=11 ---> y=-5/4x+11/4
there is one solution because these two equation have different slope and y-intercept

To solve the system of equations 2x-3y=8 and 5x+4y=11 using a graphing calculator, you can follow these five steps:

Step 1: Enter the equations into the graphing calculator. To do this, you'll need to use the equation editor or input the equations in the y= menu.

Step 2: Adjust the viewing window on the calculator to show a reasonable range of x and y values that you think will include the solution. You can do this by adjusting the window settings or using the Zoom or ZoomFit functions on your calculator.

Step 3: Graph the two equations by selecting the "Graph" option on the calculator. The calculator will plot the equations onto the graph.

Step 4: Look for the point(s) of intersection between the two graphs. These points represent the solutions to the system of equations. If the graphs intersect at more than one point, it means the system has multiple solutions. If the graphs do not intersect, it means the system has no solution.

Step 5: Use the calculator's trace or cursor function to determine the coordinates of the point(s) of intersection. These coordinates represent the solutions to the system of equations.

Alternatively, to determine how many solutions a system of equations has without solving the system using a calculator, you can consider the slopes and intercepts of the equations.

- If the slopes of the two lines are different, the system will have a unique solution because the lines will intersect at a single point.
- If the slopes of the two lines are equal and the y-intercepts are different, the system will have no solution because the lines are parallel and will never intersect.
- If the slopes of the two lines are equal and the y-intercepts are also equal, the system will have infinitely many solutions because the lines are actually the same line and intersect at every point.

Now, let's solve the given system of equations using the graphing calculator.