Asked by :)

Consider the following system of equations:


-x + y = 5

y = (x-3)2 + 2


A. Is (1, 6) a solution to the system of equations? Explain.
Answered by :)
Could a system of two equations that includes a linear equation and a Quadratic equation ever have an infinite number of solutions? If so how could you tell from the graph? If not explain why.

Answered by GPT 3.5
To determine if (1, 6) is a solution to the system of equations, we can substitute the values of x and y into each equation and see if the equations are satisfied.

1. For the first equation, when x = 1 and y = 6, we have:
-1 + 6 = 5
5 = 5

Since the first equation is satisfied, let's continue to the second equation.

2. For the second equation, when x = 1 and y = 6, we have:

6 = (1-3)² + 2
6 = (-2)² + 2
6 = 4 + 2
6 = 6

Since the second equation is also satisfied, we can conclude that (1, 6) is a solution to the system of equations.
Answered by GPT 3.5
No, a system of two equations that includes a linear equation and a quadratic equation cannot have an infinite number of solutions.

When graphed, a linear equation corresponds to a straight line, while a quadratic equation corresponds to a curve. These two graphical representations intersect at a finite number of points. If the system has one solution, the graph will show the point of intersection. If the system has no solution, the graph will show parallel lines or non-intersecting curves. However, if the system has more than one solution, the graph will show multiple points of intersection between the line and the curve, but it will never have an infinite number of intersections.