How do you solve the system by the method of substitution? x^2-y^2=9 x-y=1

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We have to solve the following system of equations by substitution.

  • x^2 - y^2 = 9
  • x - y = 1

x - y = 1

=> x = 1 + y

Substitute this for x in x^2 - y^2 = 9

=> (1 + y)^2 - y^2 = 9

=> 1 + y^2 + 2y - y^2 = 9

=> 1 + 2y = 9

=> 2y = 8

=> y = 4

x = 1 + y

=> 1 + 4

=> 5

We get x = 5 and y = 4

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giorgiana1976 | Student

We'll write the first equation as a difference of squares:

x^2-y^2=9

(x-y)(x+y)=9

We'll substitute the second equation into the first:

1*(x+y)=9

x + y = 9

We'll change the second equation and we'll write y with respect to x.

y = x - 1

But x + y = 9

x + x - 1 = 9

2x - 1 = 9

2x = 10

x = 5

y = 5 - 1

y = 4

The solution of the system is: {5 ; 4}.

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