Question

Solve by substitution

y = -x^2 + 4
y = 2x + 1

Answer 1

To solve this system of equations by substitution, express one variable in terms of the other and substitute it into the other equation. Solve the resulting quadratic equation to find the values of y.

Step-by-step explanation:

To solve this system of equations by substitution, we can express one variable in terms of the other and substitute it into the other equation.

Given equations:

y = -x^2 + 4

y = 2x + 1

1. Solve equation 2 for x: x = (y - 1) / 2
2. Substitute this expression for x in equation 1:

y = -(y - 1)^2/4 + 4

1. Simplify and solve for y:

4y = -(y - 1)^2 + 16

Solving this quadratic equation will give us the values of y.