Question

PLEASE HELP!

Answer 1

The correct option is $\boxed{{\mathbf{Option D}}}$.

Further explanation:

The system of the linear equation can be solved by the elimination method and substitution method.

Given:

Teacher gave a system of linear equation to her students Goku and Selina.

The system of linear equation has given by the teacher is written below.

$\begin{aligned}- 2x + 5y &= 10 \hfill\\-3x + 9y&= 6 \hfill\\\end{aligned}$  

The system of linear equation has found by the Goku is written below.

$\begin{aligned}x - 3y &= - 2 \hfill\\- 2x + 5y &=- 7 \hfill\\\end{aligned}$  

The system of linear equation has found by the Selina is written below.

$\begin{aligned}- 5x + 14y &= 16 \hfill \\- 3x + 9y &= 12 \hfill \\\end{aligned}$  

Step by step explanation:

Step 1:

First solve the equation has given by the teacher.

$\begin{aligned}- 2x + 5y &= 10 \hfill \\- 3x + 9y &= 6 \hfill\\\end{aligned}$  

The second equation of the above system can be written as,

$- x + 3y = 2$  

Now multiply the equation $- x + 3y = 2$ with 2.

$- 2x + 6y = 4$  

Now use elimination method to solve the system of equation.

$\begin{aligned}- 2x + 6y &= 4\hfill\\\underline { - 2x + 5y &= 10}\hfill\\{\text{ }}y& = - 6 \hfill\\\end{aligned}$  

Now substitute the value of $y = - 6$ in to equation $- 2x + 5y = 10$ to obtain the value of $x$  

$\begin{aligned}- 2x + 5\left( { - 6} \right) &= 10\\- 2x - 30 &= 10\\- 2x &= 10 + 30\\x &= - 20 \\\end{aligned}$  

Therefore, the solution of teacher’s system of the equation is $\left( { - 20, - 6} \right)$.

Step 2:

Now solve the equation has found by Goku.

$\begin{aligned}x - 3y&= - 2 \hfill\\- 2x + 5y &= - 7 \hfill\\\end{aligned}$  

Now multiply the equation $x - 3y = - 2$ with 2.

$2x - 6y = - 4$  

Now use elimination method to solve the system of equation.

$\begin{aligned}{\text{ }}2x - 6y &= - 4 \hfill\\\underline { - 2x + 5y &= - 7} \hfill \\{\text{ }} - y &= - 11 \hfill \\\end{aligned}$  

Therefore, the value of $y = 11$.

Now substitute the value of $y = 11$ in to equation $x - 3y = - 2$ to obtain the value of $x$.  

$\begin{aligned}x - 3\left( {11} \right) &= - 2\\x - 33 &= - 2\\x &= - 2 + 33\\x &= 31\\\end{aligned}$  

Therefore, the solution of Goku’s system of the equation is $\left( {31,11} \right)$.

Step 3:

Now solve the equation has found by Selina.

$\begin{aligned}- 5x + 14y&= 16 \hfill\\- 3x + 9y &= 12 \hfill\\\end{aligned}$  

The second equation of the above system can be written as,

$\begin{aligned}- 3x + 9y&= 12\\3\left({ - x + 3y} \right) &= 3\left( 4 \right)\\- x + 3y &= 4\\\end{aligned}$  

Now multiply the equation $- x + 3y = 4$ with $- 5$.

$\begin{aligned}- \left({ - 5} \right)x + \left({ - 5} \right)3y &= \left( { - 5} \right)4\\5x - 15y&= - 20\\\end{aligned}$  

Now use elimination method to solve the system of equation.

$\begin{aligned}- 5x + 14y &= 16 \hfill \\\underline {{\text{ }}5x - 15y &= - 20} \hfill\\ {\text{ }} - y &=- 4 \hfill\\\end{aligned}$  

Therefore, the value of $y = 4$ .

Now substitute the value of  $y = 4$ in to equation $- 5x + 14y = 16$ to obtain the value of  

$\begin{aligned}- 5x + 14\left( 4 \right) &= 16\\- 5x + 56 &= 16\\- 5x &= 16 - 56\\- 5x &= - 40\\x &= 8\\\end{aligned}$  

Therefore, the solution of Selina’s system of the equation is $\left( {16,4} \right)$.

Thus,  it can be seen that neither Goku nor Selina has the same solution as the teacher system.

Therefore, the correct option is $\boxed{{\mathbf{Option D}}}$.

Learn more:  

1. Learn more about the solution of the linear equation brainly.com/question/11744034
2. Learn more about the problem of the linear equation brainly.com/question/2550559
3. Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear system of equations.

Keywords: Selina, Goku, teacher, linear equation, system, elimination method, substitution, solution, multiply, divide, numbers, option

Answer 2

The answer is D Neither Goku nor Selina