The line y = 2x - 1 intersects the curve y = x^2 - 4x + 4 at two distinct points, (x_1, y_… — JAMB UTME

The line $y = 2x - 1$ intersects the curve $y = x^2 - 4x + 4$ at two distinct points, $(x_1, y_1)$ and $(x_2, y_2)$ . Calculate the sum of the $y$ -coordinates of these two points of intersection, $y_1 + y_2$ .

Answer: 10

Answer

The sum of the

y

-coordinates of the points of intersection is 10.

Equating

y = 2x - 1

and

y = x^2 - 4x + 4

yields

x^2 - 6x + 5 = 0

, whose solutions are

x = 1

and

x = 5

. Substituting these values into

y = 2x - 1

gives

y_1 = 1

and

y_2 = 9

. The sum

y_1 + y_2 = 1 + 9 = 10

Step-by-Step Solution

Equate the linear and quadratic equations to eliminate

y

x^2 - 6x + 5 = 0

Setting

2x - 1 = x^2 - 4x + 4

allows finding the

x

-coordinates of the intersection points.

Solve the quadratic equation for

x

x_1 = 1

and

x_2 = 5

Factoring

(x - 1)(x - 5) = 0

yields the two

x

-values.

Determine the corresponding

y

-values using

y = 2x - 1

y_1 = 1

and

y_2 = 9

Substituting

x = 1

yields

y = 1

, and substituting

x = 5

yields

y = 9

Calculate the sum of the

y

-coordinates.

Adding

y_1 + y_2 = 1 + 9 = 10

Key Concept

Solving simultaneous linear and quadratic equations to find coordinates of intersection

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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