Solve the system of equations. x−y=−1 and y=x^2+1

Question

Solve the system of equations.

x−y=−1

y=x^2+1

Answer 1

To solve the system of equations, we can use the substitution method. We can substitute the expression for y from the first equation into the second equation:

x - y = -1 y = x^2 + 1

First, let's rewrite the first equation to solve for y:

y = x + 1

Now, we can substitute this expression for y into the second equation:

x + 1 = x^2 + 1

Now, we have a quadratic equation in terms of x. We can solve for x by setting the equation to zero:

x^2 - x = 0

Factor out an x:

x(x - 1) = 0

This gives us two possible values for x:

x = 0 x = 1

Now, we can find the corresponding values for y using the expression y = x + 1:

For x = 0: y = 0 + 1 y = 1

For x = 1: y = 1 + 1 y = 2

So we have two solutions for the system of equations:



(x, y) = (0, 1) and (x, y) = (1, 2)