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
.