Question

In which of the following ways are linear systems similar to quadratic systems? Select all that apply.

A. Both can be solved by graphing.
B. Both can have two solutions.
C. Both can be solved by substitution.
D. Both have solutions at the points of intersection.

Answer 1

Answer: A. Both can be solved by graphing.

C. Both can be solved by substitution.

D. Both have solutions at the points of intersection.

Explanation:

Linear systems and quadratic systems both are solved by graphing and substitution.

We can graph both the systems. In linear systems , we get lines and in quadratic systems we get curves .

The points of intersection of two lines or curves are the solutions of the respectively system.

We can substitute the value of one variable in the equation find the solution .

Answer 2

The correct answers are:

A) Both can be solved by graphing;

C) Both can be solved by substitution; and

D) Both have solutions at the points of intersection.

Explanation:

Just as a system of linear equations can be solved by graphing, a system of quadratic equations can as well. We graph both equations. We then look for the intersection points of the graphs; these intersection points will be the solutions to the system.

We can also solve the system by substitution. If we can get one variable isolated, we can substitute this into the other equation to solve.