Answer
$(0, 1)$
Work Step by Step
We will use substitution to solve this system of equations. We substitute one of the expressions for $y$, which would mean that we are going to set the two equations equal to one another to solve for $x$ first:
$x^2 + 5x + 1 = x^2 + 2x + 1$
We want to move all terms to the left side of the equation.
$x^2 - x^2 + 5x - 2x + 1 - 1 = 0$
Combine like terms:
$3x = 0$
Divide each side by $3$:
$x = 0$
Now that we have the possible value for $x$, we can plug them into one of the original equations to find the corresponding $y$ value. Let's use the second equation:
$y = x^2 + 2x + 1$
Substitute the solution $0$ for $x$:
$y = 0^2 + 2(0) + 1$
Evaluate exponent first:
$y = 0 + 2(0) + 1$
Multiply to simplify:
$y = 0 + 0 + 1$
Add from left to right:
$y = 1$
The solution is $(0, 1)$.
