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.

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.