Mathematics, 18.07.2019 07:00, Jana1517

Fabiano and sonali's teacher gave them a system of linear equations to solve. they each took a few steps that led to the systems shown in the table below.

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Question: Which system has the same solution as the teacher's system?

Systems of equations that have the same solution are called equivalent systems.We are given with a system of two equations, we can make an equivalent system by substituting one equation by the sum of the two equations.

Given System:

8x-16y=14→eq.1
−x+5y=−3→eq.2
Teacher's Solution:
From eq.2
x = 5y + 3
Substituting the value of x in eq.1
We get,
8(5y + 3) - 16y = 14
40y + 24 - 16y = 14
24y + 24 = 14
24y = 14-24
24y = -10
y = -10/24
y = -5/12

Substituting y-value in eq.2,
−x+5(-5/12) = −3
-x -25/12 = -3
-x = -3 + 21/12
-x = 15/12
x = -5/4

Fabiano:
3x−15y=9
8x−16y=−7

Rearranging both equations:
y = 1/5x - 3/5
y = 1/2x+7/16

Placing both equations equal to each other,
1/5x - 3/5= 1/2x+7/16
1/5x -1/2x = 7/16 +3/5
-3/5x = 83/80
x = -83×5/80×3
x = -415/240
x = -83/48
This doesnt matches the teachers solution so we will move to sonali.

Sonali
−x+5y=−3
−4x+8y=−7
Rearranging both equations:
y = 1/5x - 3/5
y = 1/2x -7/8

Placing both equations equal to each other,
1/5x - 3/5 = 1/2x -7/8
1/5x -1/2x = -7/8 +3/5
-3/10x = -11/40
x = 110/120
x = 11/12

This doesn't match the teacher's solution either, so we will conclude that none of the solutions to the system of equation has the same answer as the teacher.

Fabiano and sonali's teacher gave them a system of linear equations to solve. they each took a few s

Fabiano and sonali's teacher gave them a system of linear equations to solve. they each took a few s

answered: damienwoodlin6

Fabiano and Sonali both have different solution with teacher’s solution.

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 Fabiano and Sonali.

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

$\begin{aligned}8x+16y=14\\-x+5y=3\end{aligned}$

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

$\begin{aligned}3x-15y=9\\8x-16y=-7\end{aligned}$

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

$\begin{aligned}-x+5y=-3\\-4x+8y=-7\end{aligned}$

Step by step explanation:

Step 1:

Teacher’s solution:

First solve the equation has given by the teacher.

$\begin{aligned}8x-16y=14\\-x+5y=-3\end{aligned}$

Now multiply the equation -x+5y=-3 with 8.

- 8x + 40y = - 24

Now use elimination method to solve the system of equation.

$\begin{aligned}{\text{}}8x - 16y &= 14 \hfill \\\underline { - 8x + 40y &= - 24}\hfill \\{\text{24}}y &= - 10 \hfill \\ \end{aligned}$

Therefore, the value of can be calculated as,

$\begin{aligned}24y&=-10\\y&=-\dfrac{-10}{24}\\y&=-\dfrac{5}{12}\end{aligned}$

Now substitute the value of $y=-\dfrac{5}{12}$ in to equation -x+5y=-3 to obtain the value of

$\begin{aligned} - x + 5\left({ - \dfrac{5}{{12}}} \right) &= - 3\\-x-\dfrac{25}{12}&=-3\\x&=3-\dfrac{25}{12}\\x&=-\dfrac{5}{4}\end{aligned}$

Therefore, the solution of teacher’s system of the equation is $\left(-\dfrac{5}{4},-\dfrac{5}{12}\right)$ .

Step 2:

Fabiano’s solution

Now solve the equation has found by Fabiano.

$\begin{aligned}3x-5y&=9\\8x-16y&=-7\end{aligned}$

Divide the first equation of the above system of linear equation by 3.

$\begin{aligned}\dfrac{3}{3}x-\dfrac{15}{3}y&=\dfrac{9}{3}\\x-5y&=6\end{aligned}$

Divide the first equation of the above system of linear equation by .

$\begin{aligned}\dfrac{8}{-8}x-\dfrac{16}{-8}y&=\dfrac{-7}{-8}\\-x+2y&=\dfrac{7}{8}\end{aligned}$

Now use elimination method to solve the system of equation.

$\begin{aligned}{\text{}}x - 5y &= 6 \hfill\\\underline { - x + 2y &= \frac{7}{8}}\hfill \\{\text{}} - 3y &= \dfrac{{41}}{8} \hfill \\\end{aligned}$

The value of can be calculated as,

$\begin{aligned}-3y&=\frac{41}{8}\\y&=-\frac{41}{8}\times\frac{1}{3}\\y&=-\frac{41}{24}\end{aligned}$

Therefore, the value of $y=-\dfrac{41}{24}$ .

It can be seen that the solution of does not match with teacher’s solution therefore, there is no need to solve the further solution.

Step 3:

Selina’s solution:

Now solve the equation has found by Sonali.

$\begin{aligned}-x+5y&=-3\\-4x+8y&=-7\end{aligned}$

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

$x-2y=\dfrac{7}{4}$

Now use elimination method to solve the system of equation.

$\begin{aligned}- x + 5y &= - 3 \hfill \\\underline {{\text{}}x - 2y&= \frac{7}{4}}\hfill \\{\text{3}}y &=- \frac{5}{4} \hfill \\\end{aligned}$

The value of can be calculated as,

$\begin{aligned}3y&=-\dfrac{5}{4}\\y&=-\dfrac{5}{4}\times\dfrac{1}{3}\\y&=-\dfrac{5}{12}\end{aligned}$

Therefore, the value of $y=-\dfrac{5}{12}$ .

Now substitute the value of $y=-\dfrac{5}{12}$ in to equation $x-2y=\dfrac{7}{4}$ to obtain the value of

$\begin{aligned}x-2\left(-\dfrac{5}{12}\right)&=\dfrac{7}{4}\\x+2\left(\dfrac{5}{12}\right)&=\dfrac{7}{4}\\\x&=\dfrac{7}{4}-\dfrac{5}{6}\\x&=\frac{42-20}{24}\end{aligned}$

Further simplify the above equation.

$\begin{aligned}x=\dfrac{22}{24}\\x=\dfrac{11}{12}\end{aligned}$

The solution of Sonali’s system of the equation is $\left(\dfrac{11}{12,}-\dfrac{5}{12}\right)$ .

Therefore, it can be seen that the solution of Sonali does not match with teacher’s solution.

Thus, both the students have different solution with teacher’s solution.

Learn more:

Learn more about the solution of the linear equation Learn more about the problem of the linear equation Learn more about equations of the area and perimeter of the rectangle

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear system of equations.

Keywords: Sonali, Fabiano, teacher, linear equation, system, elimination method, substitution, solution, multiply, divide, numbers, option.

answered: Guest

The correct graph is the second one, with the points being at (-6,0), (2,0) and reaching down to (-2,-8)

answered: Guest

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