Answer:
(-2, 5) and (1, 2)
Explanation:
To solve the system of equations set the right side expressions of f(x) equal to each other and solve for x
x² + 1 = -x + 3
Add x to both sides:
x² + 1 + x = -x + x + 3
x² + 1 + x= 3
Rearrange:
x² + x + 1 = 3
Subtract 3 from both sides:
x² + x + 1 - 3 = 0
x² + x -2 =0
This is a quadratic equation which can be easily solved by factoring the expression on the left side
x² + x - 2 = (x - 1)(x + 2)
Setting the factored expression = 0 gives
(x - 1)(x + 2) = 0
This means
x - 1 = 0 ==> x = 1 is one solution
x + 2 = 0 ==> x = -2 is another solution
Smaller value of x is x = -2
Substitute these values of x into any one equation and find the resultant f(x) value. Equation 2 is easier to deal with
At x = -2, f(x) = -x + 3 is - (-2) + 3 = 2 + 3 = 5
So (-2, 5) is one ordered pair solution
At x = 1 , f(x) = -x + 3 is -1 + 3 = 2
So (1, 2) is another ordered pair solution
The two ordered pair solutions are
(-2, 5) and (1, 2)