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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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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