Match the system of equations to the number of solutions it has. You can use your Graphing Calculator! (4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. y = 5x + 7 3y - 15x = 18 y = 3x + 6 y = -13x - 4 x - 2y = 6 3x - 6y = 18 y = 23x - 1 y = 23x - 2
The system of equations: y = 5x + 7
The system of equations: 3y - 15x = 18
The system of equations: y = 3x + 6
The system of equations: y = -13x - 4
The system of equations: x - 2y = 6
The system of equations: 3x - 6y = 18
The system of equations: y = 23x - 1
The system of equations: y = 23x - 2
This system of equations has 1 solution: y = -13x - 4 and x - 2y = 6
This system of equations has infinitely many solutions: y = 5x + 7 and 3y - 15x = 18
This system of equations has 1 solution: y = 3x + 6 and 3x - 6y = 18
This system of equations has no solution: y = 23x - 1 and y = 23x - 2.
To determine the number of solutions each system of equations has, we can use a graphing calculator.
First, let's input the first system of equations:
y = 5x + 7
3y - 15x = 18
The graphing calculator will show us the graph of these two equations.
Next, let's input the second system of equations:
y = 3x + 6
x - 2y = 6
Again, we will see the graph of these two equations.
For the third system of equations:
3x - 6y = 18
y = 23x - 1
We will input these equations into the calculator, and observe the graph.
Lastly, for the fourth system of equations:
y = 23x - 2
We will input this equation and examine the graph.
By interpreting the graphs, we can determine the number of solutions for each system of equations.
To determine the number of solutions for each system of equations, we can use our Graphing Calculator. Here's how to do it:
1. Enter the first system of equations: y = 5x + 7 and 3y - 15x = 18.
2. Graph the equations by entering them into the calculator and pressing the appropriate buttons to plot them.
3. Observe the graph. If the lines intersect at a single point, the system has exactly one solution. If the lines are parallel and do not intersect, the system has no solution. If the lines coincide and overlap, the system has infinitely many solutions.
Now, let's analyze each system of equations provided:
System 1: y = 5x + 7 and 3y - 15x = 18
- Enter the equations into the calculator and graph them.
- Observe the graph. If the lines intersect at one point, select "One Solution." If they are parallel, select "No Solution." If they overlap and coincide, select "Infinite Solutions."
System 2: y = 3x + 6 and x - 2y = 6
- Enter the equations into the calculator and graph them.
- Observe the graph to determine the number of solutions by selecting the appropriate answer.
System 3: y = -13x - 4 and 3x - 6y = 18
- Follow the same process as before to determine the number of solutions.
System 4: y = 23x - 1 and y = 23x - 2
- Enter the equations into the calculator and graph them.
- Observe the graph and select the correct response based on the number of solutions.
By following this step-by-step process, you can match each system of equations to the number of solutions it has.