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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

Verified Answer :

taskmasters

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. 

carlosego

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

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