Question

Pablo graphs a system of equations. One equation is quadratic and the other equation is linear. What is the greatest number of possible solutions to this system?

a.0
b.1
c.2
d.4

Answer 1

The answer would be option c. A quadratic equation and a linear equation only involves two variables, an independent variable and a dependent variable. Therefore, having these two equation, the greatest number of possible solutions to this system is two.

Answer 2

For this case we have the following type of equations:
Quadratic equation:

`y = ax ^ 2 + bx + c`
Linear equation:

`y = mx + b`
We observe that when equating the equations we have:

`ax ^ 2 + bx + c = mx + b`
Rewriting we have:

`ax ^ 2 + (b-m) x + (c-b) = 0`
We obtain a polynomial of second degree, therefore, the maximum number of solutions that we can obtain is 2.
Answer:
The greatest number of possible solutions to this system is:
c.2