Write a system of two equations in two variables where one equation is quadratic and the other is linear such that the system has no solution. explain, using graphs, algebra, and/or words, why the system has no solution.

This system has no solution:

y = x²

y = 0 · x - 1

Step-by-step explanation:

Hi there!

I propose these two equations:

y = x²

y = 0 · x - 1

This system has no solution because in the quadratic function "y" is always positive for every value of "x", while in the linear function "y" is always -1 for every value of "x". Then, there will not be a pair (x,y) shared by both functions.

In other words, there is no value of "x" that satisfies this expression:

x² = 0 · x - 1

In the attached graphic, you can see that both curves never touch (in red is the quadratic function and in blue is the linear function), hence, the system has no solution.

Have a nice day!

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this