Write a system of equations with the solution (4, -3)

Answer 1

The problem does not specify a system of linear equations, but let us presume that is what is being requested.

Let x=4, which is a vertical line going through the point (4,-3).

Now consider y=-3, which is a horizontal line also going through the point (4,-3).

So the system of linear equations

x = 4

y = -3

has the unique intersection point and solution (4,-3).

Mission accomplished. Depending upon your point of view, you might consider this lazy or you might see it see it as elegant. But you can't deny it solves the problem as stated.

Answer 2

Sure, you can create a system of equations with the solution (4, -3) using the point-slope form of a line equation, which is y - y1 = m(x - x1).

For the point (4, -3), any line that passes through this point can be described as:

y + 3 = m(x - 4)

You can rearrange this to:

y = m(x - 4) - 3

Now, you can choose different slopes (m) to create different equations. For example, if you pick m = 2 for the first equation and m = -1 for the second equation, the equations become:

1. y = 2(x - 4) - 3
2. y = -1(x - 4) - 3

Or, when simplified:

1. y = 2x - 11
2. y = -x + 1

You can create infinitely many such systems by choosing different slopes.

Answer 3

3x - 5y = 27

-2x + y = -11