solve the system of equations
y = x + 4
y = x^2 + 9x +16
x^2 + 9x +16 = x + 4
x^2 + 9x -x + 16 - 4 = -(x+4)
x^2 + 8x + 12 = 0
(x +2)(x+6) = 0
solve for x
x + 2-2 = 0 -2
x = -2
x - 6 -6 = 0-6
x = -6
(-2, 2), (-6 ,-2)
Typo
x + 6 -6 = 0-6
x = -6
To solve the system of equations, we'll use the method of substitution by substituting one equation into the other. Let's substitute the value of y from the first equation into the second equation:
Substituting y = x + 4 into the second equation:
x + 4 = x^2 + 9x + 16
Now we can set this quadratic equation equal to zero:
x^2 + 8x + 12 = 0
To solve this quadratic equation, we can factor it:
(x + 2)(x + 6) = 0
Setting each factor equal to zero:
x + 2 = 0 or x + 6 = 0
Solving for x:
x = -2 or x = -6
Now that we have the values of x, we can substitute them back into the first equation to find the corresponding values of y.
For x = -2:
y = x + 4
y = -2 + 4
y = 2
For x = -6:
y = x + 4
y = -6 + 4
y = -2
Therefore, the solution to the system of equations is x = -2, y = 2 and x = -6, y = -2.