given the equation -3x +2y =4, Write another equation that will form a linear system with:

one solution, no solution and infinite solution.
Graph the linear using graphing calculator and write your window setting in the format
x: Xmin, xmax, Xscl. Y: Ymin, Ymax, Yscl

Please correct if there any mistake and how do you write the window setting?

answer:

one solution:
y= 3/2x + 2
y= -3/2x +4

no solution:
y=3/2x+2
y=3/2x - 3

infinite solution:

(-3x +2y =) * 3 -> -9x +6y =12

y=3/2x+2
-9x +6y =12

Yes, all the equations you wrote are correct. :)

I don't know what window setting means too, and I don't have a graphing calculator. But I think window setting looks like in table (rows,columns) format? I'm not really sure. ^^;

Thank you =)

=I will try to search about it, how to write these window setting for graphing.

To write another equation that will form a linear system with one solution, you need to find another equation that intersects the line represented by the equation -3x + 2y = 4 at a unique point.

To do this, you can start by rearranging the equation -3x + 2y = 4 to solve for y:
2y = 3x + 4
y = (3/2)x + 2

Now, you can create another equation by simply changing the coefficients or constants. For example, you can rewrite the equation as:
y = -(3/2)x + 4

This equation will have a unique solution because it intersects the line -3x + 2y = 4 at one point.

To form a linear system with no solution, you need to find another equation such that it represents a parallel line to -3x + 2y = 4. Parallel lines never intersect, so the system will have no solution.

Using the same equation, -3x + 2y = 4, you can keep the coefficients the same but change the constant term. For example, you can rewrite the equation as:
-3x + 2y = -3

This equation will have no solution because it represents a parallel line to the original equation -3x + 2y = 4.

To form a linear system with infinite solutions, you need to find another equation that represents the same line as the equation -3x + 2y = 4. Since both equations would represent the same line, they will intersect at every point and have infinitely many solutions.

Again, using the same equation, -3x + 2y = 4, you can create another equation by multiplying all terms by a constant. For example, multiplying both sides of the equation by 3 would give you:
-9x + 6y = 12

This equation represents the same line as the original equation, -3x + 2y = 4. Therefore, the two equations form a linear system with infinitely many solutions.

To graph these linear equations on a graphing calculator, you will need to set up the window settings appropriately.

Window settings format:
X: Xmin, Xmax, Xscl
Y: Ymin, Ymax, Yscl

The window settings determine the range and precision of the x and y-axis values that will be displayed on the graph.

Setting the window settings depends on the range of x and y values you want to display on the graph. It's recommended to find the x and y intercepts of the linear equations to get an idea of the range.

For this particular example, a suitable window setting could be:
X: -10, 10, 1
Y: -10, 10, 1

This means that the x-axis will be displayed from -10 to 10, with a scale of 1. Similarly, the y-axis will be displayed from -10 to 10, with a scale of 1.

Remember that window settings can be adjusted based on the specific needs of the graph and the range of values you want to display.