Solve the simultaneous equations y = 2x + 1 and y = x^2 - 2. Which of the following repres… — JAMB UTME

Solve the simultaneous equations $y = 2x + 1$ and $y = x^2 - 2$ . Which of the following represents the complete set of solution pairs $(x, y)$ ?

The complete set of solution pairs

(x, y)

(3, 7)

and

(-1, -1)

Equating

2x + 1 = x^2 - 2

yields

x^2 - 2x - 3 = 0

. Factoring gives

(x - 3)(x + 1) = 0

, leading to

x = 3

x = -1

. Substituting these

x

-values into

y = 2x + 1

gives

y = 7

for

x = 3

, and

y = -1

for

x = -1

. Thus, the solution pairs are

(3, 7)

and

(-1, -1)

Equate the linear expression for

y

to the quadratic expression for

y

2x + 1 = x^2 - 2

Since both expressions equal

y

, setting them equal eliminates

y

Rearrange the equation into standard quadratic form

ax^2 + bx + c = 0

x^2 - 2x - 3 = 0

Subtract

2x

and

1

from both sides.

Factor the quadratic equation to find the values of

x

(x - 3)(x + 1) = 0 \implies x = 3 \text{ or } x = -1

Determine two numbers that multiply to

-3

and add to

-2

Substitute each

x

-value back into the linear equation

y = 2x + 1

to find the corresponding

y

-value.

For

x = 3

y = 2(3) + 1 = 7

. For

x = -1

y = 2(-1) + 1 = -1

Calculate the exact coordinate pairs

(x, y)

that satisfy both equations.

Solving simultaneous linear and quadratic equations using algebraic substitution.

Question