heeelp3

Question

Determine the coordinates of the point of the intersection of the linear quadratic system below algebraically. show how to check

a. y=x²-7x+15,  y=2x-5

b. y=3x+5,  y=2x²+4x-1

c. y=2x²-2x+1,  y=3x-5

Answer 1

Step 1 :

a.

The linear quadratic system is and .

Substitute in .

Step 2 :

Solve the equation .

Factorize the quadratic equation.

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 pioint in .

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

Solution :

The intersection points are and .

Answer 2

Step 1 :

b.

The linear quadratic system is and .

Substitute in .

Step 2 :

Solve the equation .

Factorize the quadratic equation.

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 .

Answer 3

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 :

.

Since the x - values are the imaginary values, there is no real solutions for the linear quadratic system and .

Solution :

There is no real solutions for the linear quadratic system and .