Question

X² +2=y
2x+y=1
Use substitution to solve

Answer 1

The solution to the system of equations using substitution is x = -1 and y = 3. Solve y from the first equation and substitute into the second, simplify, factor the quadratic, and find the value of x, then find y.

Step-by-step explanation:

To solve the system of equations x² + 2 = y and 2x + y = 1 using substitution, we start by expressing one variable in terms of the other from the first equation.

Then, we substitute this expression into the second equation to find the value of the other variable.

1. From the first equation, solve for y: y = x²+2.
2. Substitute this expression for y in the second equation: 2x + (x² + 2) = 1.
3. Simplify the second equation: x² + 2x + 2 = 1.
4. Bring all terms to one side to form a quadratic equation: x² + 2x + 1 = 0.
5. Factor the quadratic equation: (x + 1)(x + 1) = 0.
6. Find the solution for x: x = -1.
7. Substitute x back into y = x² + 2 to find y: y = (-1)² + 2 = 3.

The solution to the system is x = -1 and y = 3.