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15 votes
15 votes
Solve the simultaneous equations.
x^2+y^2=13
y=x+1

User Do Tat Hoan
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1 Answer

14 votes
14 votes

Answer:

x² + y² = 13 ---1

y = x + 1 ---2

First make one of the unknowns the subject so you can substitute it into the other equation. Since 2 already has y as the subject, we can substitute 2 into 1 to find x.

Substitute 2 into 1:

x² + (x +1)² = 13

x² + (x² + 2x + 1) = 13

2x² + 2x - 12 = 0

2 is a common factor so we factorize it out.

2(x² + x - 6) = 0

x² + x - 6 = 0

Factorize the equation further.

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

x - 2 = 0 or x + 3 = 0

x = 2 or x = - 3

Substitute values of x into 2 to find y.

y = 2 + 1 or y = - 3 + 1

= 3 = - 2

Hence, x = 2 and y = 3 or x = - 3 and y = - 2.

User Bwmat
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