Question

Which of the following values are in the range of the function graphed below?Check all that apply.10+-10. 1002O A. -1OB. 2O C. 1O D. -6E. -2

Answer 1

The answer is (5, - 4) (Option D)

We are required to solve the system of equations:

`\begin{gathered} 4x+y=16\text{ (Equation 1)} \\ 2x+3y=-2\text{ (Equation 2)} \end{gathered}`

In order to solve the equations, we need to make sure that one of the terms in both equations is the same.

In (Equation 1), there is a 4x term. In (Equation 2), there is a 2x term.

We can make 2x in (Equation 2), the same as 4x in (Equation 1), by multiplying the whole of (Equation 2) by 2

Let us perform this multiplication below:

`\begin{gathered} 4x+y=16\text{ (Equation 1)} \\ 2x+3y=-2\text{ (Equation 2)} \\ \text{ Multiply (Equation) 2 by 2} \\ 2*(2x+3y)=-2*2 \\ 4x+6y=-4\text{ (Equation 3)} \\ \\ \text{Now we have two equations with 4x as a common term. They are:} \\ \\ 4x+y=16\text{ (Equation 1)} \\ 4x+6y=-4\text{ (Equation 3)} \end{gathered}`

Now that we have a similar term in both (Equation 1) and (Equation 2), we can subtract both equations to eliminate that term and then find the value of y.

This is done below:

`\begin{gathered} 4x+y=16 \\ -(4x+6y)=-(-4)_{} \\ \\ 4x+y=16 \\ -4x-6y=4 \\ \\ 4x-4x+y-6y=16+4 \\ -5y=20\text{ (Divide both sides by -5)} \\ \\ \therefore y=-(20)/(5)=-4 \end{gathered}`

Now that we have the value of y, we can substitute this value into Equation 1 to get the value of x

This is done below:

`\begin{gathered} \text{Equation 1:} \\ 4x+y=16 \\ \text{but y = -4} \\ \\ 4x+\text{ -4= 16} \\ 4x-4=16 \\ \\ \text{add 4 to both sides} \\ \\ 4x-4+4=16+4_{} \\ 4x=20\text{ (Divide both sides by 4)} \\ \\ x=(20)/(4)=5 \end{gathered}`

Therefore, the solution to the system of equations is:

x = 5, y = -4

Thus the final answer is (5, - 4) (Option D)