Chapter 5.1, Problem 2E

To determine

To choose: The odd one expression that among all the options with explanation and find both the answers.

Answer to Problem 2E

The question solve for each equation for $y$ is different question among all the questions.

Explanation of Solution

Given information:

The system of linear equations is $-4x+2y=4,4x-y=-6$ .

Calculation:

Solve the system of equations by elimination method.

  $-4x+2y=4,4x-y=-6$

Add both the equations to obtain the value of $y$ .

  $\begin{array}{l}\underset{\_}{\begin{array}{c}-4x+2y=4\\ 4x-y=-6\end{array}}\\ y=-2\end{array}$

The value of $y=-2$ .

Now substitute the value $y=-2$ in the equation $-4x+2y=4$ to obtain the value of $x$ .

  $\begin{array}{c}-4x+2\left(-2\right)=4\\ -4x-4=4\\ -4x=8\\ x=-2\end{array}$

The solutions of the system of linear equation is $x=-2,y=-2$ .

The second question is solve each equation for $y$ .

The equation can be solved for $y$ as follows:

Solve the equation $-4x+2y=4$ for $y$ .

  $\begin{array}{c}-4x+2y=4\\ 2y=4+4x\\ y=2+2x\end{array}$

Solve the equation $4x-y=-6$ for $y$ .

  $\begin{array}{c}4x-y=-6\\ 4x+6=y\\ y=4x+6\end{array}$

The equations are $y=4x+6$ and $y=2+2x$ .

Third question is find the point of the intersection of the given equations.

Intersection points are the solutions of the given system of linear equation is $x=-2,y=-2$ .

Fourth question is to find the ordered pair solution.

The ordered pair of the given system of linear equation is $\left(-2,-2\right)$ .

It can be seen the question solve for each equation $y$ is different question among all the questions.