Step 1 :
\a.
\The linear quadratic system is
and
.
Substitute
in
.

Step 2 :
\Solve the equation
.
By factoring by grouping.
\
If
, then
.
If
, then
.
The intersection points are
and
.
Check :
\Substitute the point
in

Since the above statement is true,
is a intersection point of The linear quadratic system is
and
.
Substitute the pioint 

Since the above statement is true,
is a intersection point of the linear quadratic system is
and
.
Solution :
\The intersection points are
and
.
Step 1 :
\b.
\The linear quadratic system is
and
.
Substitute
in
.

Step 2 :
\Solve the equation
.
By factoring by grouping.
\

If
, then
.
If
, then
.
The intersection points are
and
.
Check :
\To check the solution, substitute the point
in
.

Since the above statement is true,
is a intersection point of the linear quadratic system
and
.
To check the solution, substitute the point
in
.

Since the above statement is true,
is a intersection point of the linear quadratic system
and
.
Solution :
\The intersection points are
and
.
Step 1 :
\c.
\The linear quadratic system is
and
.
Substitute
in
.

Step 2 :
\Solve the equation
.
is a quadratic equation, use quadratic formula to find the solution of the related quadratic equation.
Solution
.
Compare the equation with standard form of the quadratic equation
.
.
Solution
\
.
If
, then
.
If
, then

The intersection points are imaginary points.
\They are
and
.
Check :
\To check the solution, substitute the point
in
.

Since the above statement is true,
is a intersection point of the linear quadratic system
and
.
To check the solution, substitute the point
in
.

Since the above statement is true,
is a intersection point of the linear quadratic system
and
.
Solution :
\The imaginary intersection points are
and
.