Question

Solve the system of equations:

[ Y = -x² + 4 ]
[ y = 2x + 1 ]

a) x = -1, y = -1
b) x = 1, y = 3
c) x = 2, y = 5
d) x = -2, y = -3

Answer 1

To solve the system of equations, we substitute Equation 2 into Equation 1 to eliminate the variable Y. Then, we solve the resulting quadratic equation to find the values of x. Finally, we substitute the x-values into Equation 2 to find the corresponding y-values.

Step-by-step explanation:

To solve the system of equations:

Equation 1: Y = -x² + 4

Equation 2: y = 2x + 1

We can substitute Equation 2 into Equation 1 to eliminate the variable Y:

-x² + 4 = 2x + 1

Rearranging the equation:

x² + 2x - 3 = 0

Factoring the quadratic equation:

(x + 3)(x - 1) = 0

Solving for x:

x = -3, x = 1

Substituting the x-values into Equation 2 to find the corresponding y-values:

For x = -3, y = 2(-3) + 1 = -5

For x = 1, y = 2(1) + 1 = 3

Therefore, the solutions to the system of equations are:

x = -3, y = -5

x = 1, y = 3