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Topic: Nonlinear Systems of EquationsCreate a system of equations that includes one linear equation and one quadratic equation.Show all work in solving your system of equations algebraically.

User QIBIN LI
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1 Answer

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Answer:

• Equations


y=x+2
y=x^2

• Solutions (2, 4) and (–1, 1)

Step-by-step explanation

System of equations

• Linear equation


y=x+2

• Quadratic equation


y=x^2

We have to set both equations to 0 and equalize them:

• 1. Setting them to 0:


0=x+2
0=x^2

• 2. Equalizing them:


x+2=x^2

To solve the system using the General Quadratic Formula, we have to set the equation in the form ax² + bx+ c = 0:


x^2-x-2=0

Thus, in this case a = 1, b = -1 and c = -2. Using the formula:


x_(1,2)=(-(-1)\pm√((-1)^2-4(1)(-2)))/(2(1))
x_(1,2)=(1\pm√(1+8))/(2)
x_(1,2)=(1\pm√(9))/(2)

Finding both solutions:


x_1=(1+3)/(2)=(4)/(2)=2
x_2=(1-3)/(2)=(-2)/(2)=-1

Finally, replacing these values in the linear equation to find y:


y_1=2+2=4
y_2=-1+2=1

Therefore, the solutions are (2, 4) and (–1, 1).

User MalcolmInTheCenter
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