solve the simlutaneous equation:
x^2= 4-y
x= y+2
To solve this simultaneous equation, we can use the second equation to substitute the value of x in the first equation:
x = y + 2
Substituting this value of x in the first equation:
(y + 2)^2 = 4 - y
Expanding the squared term:
y^2 + 4y + 4 = 4 - y
Rearranging the equation:
y^2 + 4y + y - 4 = 0
Combining like terms:
y^2 + 5y - 4 = 0
Now we have a quadratic equation in terms of y. To solve this equation, we can factor it or use the quadratic formula. Let's factor it:
(y - 1)(y + 4) = 0
Setting each factor equal to zero and solving for y:
y - 1 = 0 or y + 4 = 0
y = 1 or y = -4
Now that we have the values of y, we can substitute them back into the second equation to find the corresponding values of x:
For y = 1:
x = y + 2
x = 1 + 2
x = 3
For y = -4:
x = y + 2
x = -4 + 2
x = -2
Therefore, the solutions to the simultaneous equations are:
x = 3, y = 1
x = -2, y = -4