JAMB - Mathematics (1978 - No. 30)
The set of value of x and y which satisfies the equations x2 - y - 1 = 0 and y - 2x + 2 = 0 is
1, 0
1, 1
2, 2
0, 2
1, 2
Explanation
x2 - y - 1 = 0.......(i)
y - 2x + 2 = 0......(ii)
By re-arranging eqn. (ii)
y = 2x - 2........(iii)
Subst. eqn. (iii) in eqn (i)
x2 - (2x - 2) - 1 = 0
x2 - 2x + 1 = 0
= (x - 1) = 0
When x - 1 = 0
x = 1
Sub. for x = 1 in eqn. (iii)
y = 2 - 2 = 0
x = 1, y = 0
y - 2x + 2 = 0......(ii)
By re-arranging eqn. (ii)
y = 2x - 2........(iii)
Subst. eqn. (iii) in eqn (i)
x2 - (2x - 2) - 1 = 0
x2 - 2x + 1 = 0
= (x - 1) = 0
When x - 1 = 0
x = 1
Sub. for x = 1 in eqn. (iii)
y = 2 - 2 = 0
x = 1, y = 0
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