What is the positive value of x that satisfies the simultaneous equations y - x = 1 and y … — JAMB UTME

What is the positive value of $x$ that satisfies the simultaneous equations $y - x = 1$ and $y = x^2 - 5$ ?

The positive value of

x

3

Substituting

y = x + 1

from the linear equation into the quadratic equation gives

x + 1 = x^2 - 5

. Rearranging terms yields

x^2 - x - 6 = 0

, which factors as

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

. The roots are

x = 3

and

x = -2

. Selecting the positive solution gives

3

Express

y

in terms of

x

using the linear equation.

y = x + 1

Isolating

y

simplifies substitution into the quadratic equation.

Substitute

y = x + 1

into the quadratic equation

y = x^2 - 5

x + 1 = x^2 - 5

This produces a quadratic equation in one variable,

x

Rearrange into standard quadratic form

ax^2 + bx + c = 0

x^2 - x - 6 = 0

Standard quadratic form allows direct factorization.

Factorize the quadratic equation.

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

Factoring determines the roots of the equation.

Solve for

x

and identify the positive value.

x = 3

x = -2

; positive value is

3

The question specifies the positive real solution for

x

Solving simultaneous linear and quadratic equations using substitution

Question