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