Solve by Substitution x-y^2=-1 , x-2y=2

Problem

{[x−y2=−1],[x−2*y=2])

Solution

1. Isolate the variable x in the second equation to prepare for substitution.

x−2*y=2

x=2*y+2

2. Substitute the expression for x into the first equation.

(2*y+2)−y2=−1

3. Rearrange the equation into a standard quadratic form a*y2+b*y+c=0

−y2+2*y+2=−1

−y2+2*y+3=0

y2−2*y−3=0

4. Factor the quadratic equation to find the possible values for y

(y−3)*(y+1)=0

y=3

y=−1

5. Substitute each y value back into the expression x=2*y+2 to find the corresponding x values.

If *y=3⇒x=2*(3)+2=8

If *y=−1⇒x=2*(−1)+2=0

Final Answer

(x,y)=(8,3),(0,−1)

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