Solve the pair of simultaneous equations
x^2=4-y
x=y+2
To solve this pair of simultaneous equations, we can use the method of substitution.
Start by rearranging the second equation to solve for x:
x = y + 2
Now substitute this expression for x into the first equation:
(y + 2)^2 = 4 - y
Expand and simplify the equation:
y^2 + 4y + 4 = 4 - y
Combine like terms:
y^2 + 4y + y + 4 - 4 = 0
Simplify further:
y^2 + 5y = 0
Factor out the common factor:
y(y + 5) = 0
Set each factor equal to zero and solve for y:
y = 0 or y + 5 = 0
If y = 0, substitute this value back into the second equation to solve for x:
x = 0 + 2
x = 2
If y = -5, substitute this value back into the second equation to solve for x:
x = -5 + 2
x = -3
So, the solution to the pair of simultaneous equations is:
(x, y) = (2, 0) or (-3, -5)
In the second, y=x-2.
then
x^2=4-x+2
x^2+x-6=0
factor, then solve.