What is the positive value of y that satisfies the simultaneous equations x - y = 2 and x^… — JAMB UTME

What is the positive value of $y$ that satisfies the simultaneous equations $x - y = 2$ and $x^2 - y^2 = 12$ ?

The positive value of y is 2.

Factoring

x^2 - y^2

(x - y)(x + y)

gives

2(x + y) = 12

, leading to

x + y = 6

. Subtracting

x - y = 2

from

x + y = 6

isolates

2y = 4

, giving

y = 2

Factorize the quadratic difference of squares equation.

x^2 - y^2 = (x - y)(x + y) = 12

Difference of two squares identity allows linear substitution.

Substitute

x - y = 2

into the factorized expression.

2(x + y) = 12 \implies x + y = 6

Simplifies the quadratic system into a second linear equation.

Solve the system of linear equations

x + y = 6

and

x - y = 2

for

y

(x + y) - (x - y) = 6 - 2 \implies 2y = 4 \implies y = 2

Subtracting the two linear equations eliminates

x

and directly isolates

y

Simultaneous Linear and Quadratic Equations via Difference of Squares Substitution

Estimated Time:45s

Question