Question

Solve the following system of equations and show all work. y = −x2 + 4 y = 2x + 1

Answer 1

To solve the given system of equations, one equation is substituted into the other, since they are both equal to y, resulting in a quadratic equation. This quadratic equation is then solved to find the x values, which are used to determine the corresponding y values.

Step-by-step explanation:

To solve the system of equations given:

1. y = −x2 + 4
2. y = 2x + 1

We set the two equations equal to each other since they both equal y:

−x2 + 4 = 2x + 1

Now, we solve for x:

−x2 − 2x + 4 - 1 = 0

−x2 − 2x + 3 = 0

Solving this quadratic equation, we find the values of x. We can then substitute these values back into either equation to find the corresponding y values.

Answer 2

Answer: X=2, Y=5. 2, 5

Step-by-step explanation: The answer is 2, 5. I got this by first square rooting the first equation on the top to get y=-x+2. Then I subtracted the two equations and got y=x+3, I then substituted that into the second equation and solved to get x=2. I substituted x=2 into y=2x+1 and got y=5. To check I substituted in the equation 5=2(2)+1. Which equals 5 meaning my answer is correct.