Final answer:
To solve the system of equations, substitute one equation into the other and then solve for x. After finding the values of x, substitute them back into one of the original equations to find the corresponding y-values. The solutions to the system of equations are (2,8) and (-2,4).
Step-by-step explanation:
To solve the system of equations {y=x²+2 and {y=6+x, we can use the method of substitution. Since both equations are equal to y, we can set them equal to each other and solve for x.
x²+2 = 6+x
Now, we can simplify the equation by subtracting x from both sides:
x²-x+2=6
Next, subtract 6 from both sides:
x²-x-4=0
Now we can solve this quadratic equation by factoring or using the quadratic formula:
x²-x-4 = (x-2)(x+2) = 0
Setting each factor equal to zero, we find x=2 and x=-2.
Substituting these values back into either equation, we can find the corresponding y-values. When x=2, y=6+2=8. When x=-2, y=6+(-2)=4.
Therefore, the solutions to the system of equations are (2,8) and (-2,4).