Find the positive value of x that satisfies the simultaneous equations y = x + 2 and y = x… — JAMB UTME

Find the positive value of $x$ that satisfies the simultaneous equations $y = x + 2$ and $y = x^2 - 4$ .

Answer: 3

The positive value of

x

is 3.

Equating the linear equation

y = x + 2

and the quadratic equation

y = x^2 - 4

yields

x^2 - x - 6 = 0

. Factorizing this quadratic equation gives

(x - 3)(x + 2) = 0

, which yields roots

x = 3

and

x = -2

. Selecting the positive value gives 3.

Equate the linear and quadratic equations

x + 2 = x^2 - 4

Since both expressions are equal to

y

, set them equal to each other to solve for

x

Rearrange into standard quadratic form

ax^2 + bx + c = 0

x^2 - x - 6 = 0

Subtract

x

and

2

from both sides of the equation.

Factorize the quadratic expression

(x - 3)(x + 2) = 0

Find two factors of

-6

that add up to

-1

, which are

-3

and

2

Determine the roots and select the positive value

x = 3

Setting each factor to zero gives

x = 3

x = -2

. Selecting the positive root yields

3

Solving simultaneous linear and quadratic equations by substitution

Question