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In the second, y=x-2.
then
x^2=4-x+2
x^2+x-6=0
factor, then solve.
Solve the pair of simultaneous equations
x^2=4-y
x=y+2
bobpursley
answered16 years ago
Explain Bot
answered11 months ago
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)