Solve for x and y in the equations below x 2 - y 2 = 4 x + y = 2

Correct Answer is : x = 2, y = 0

Correct Answer is : x = 2, y = 0

Test Index

JAMB Mathematics 2012 Paper

Question : 12

Total: 48

x + y = 2

Solution:

Concept:

Use the difference of two squares and substitution to reduce the system to simple linear equations.

Explanation:

From

x + y = 2

, note that

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

Substitute

x + y = 2

into

x^2 - y^2 = 4

Then

2(x - y) = 4

, so

x - y = 2

Now solve the pair:

x + y = 2

and

x - y = 2

Add the equations:

2x = 4

, so

x = 2

Substitute

x = 2

into

x + y = 2

to get

y = 0

Answer:

x = 2

y = 0

This matches option C.

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