Question

PART A. What is the solution to the system of linear equations? PART B. Explain how you found the solution to the system of linear equations. PART C. What is one way you could prove your answer to PART A is correct? Show your work.

Answer 1

ANSWER and EXPLANATION

PART A

The solution to the system of linear equations is (-4, 4)

PART B

The solution to any system of graphed equations is the point on the graph where the two lines intercept.

Therefore, since f(x) and g(x) intercept at (-4, 4), it is the solution to the system of linear equations.

PART C

To prove that the answer is correct, we can solve it with another method i.e. equate the two equations and find x. The value of both functions at that value of x will be the same.

`\begin{gathered} f(x)=g(x) \\ (1)/(2)x+6=-2x-4 \\ \text{Collect like terms:} \\ (1)/(2)x+2x=-4-6 \\ (5)/(2)x=-10 \\ \text{Multiply both sides of equation by }(2)/(5)\colon \\ x=-10\cdot(2)/(5) \\ x=-4 \end{gathered}`

Find the corresponding values of f(x) and g(x):

`\begin{gathered} f(-4)=(1)/(2)(-4)+6=-2+6 \\ f(-4)=4 \\ g(-4)=-2(-4)-4=8-4 \\ g(-4)=4 \end{gathered}`

Therefore, we have proven that the answer is correct.