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
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.
For this case we have the following type of equations: Quadratic equation: [tex]y = ax ^ 2 + bx + c
[/tex] Linear equation: [tex]y = mx + b
[/tex] We observe that when equating the equations we have: [tex]ax ^ 2 + bx + c = mx + b
[/tex] Rewriting we have: [tex]ax ^ 2 + (b-m) x + (c-b) = 0
[/tex] 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
