Question

The table below shows four systems of equations:

System 1
4x − 5y = 2
3x − y = 8


System 2
4x − 5y = 2
10x − 7y = 18

System 3
4x − 5y = 2
3x − 8y = 4

System 4
4x − 5y = 2
10x + 3y = 15

Which pair of systems will have the same solution?

A. System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1

B. System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to two times the second equation in system 2

C. System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to three times the second equation in system 1

D. System 2 and system 3, because the second equation in system 3 is obtained by adding the first equation in system 2 to three times the second equation in system 2

Answer 1

Solving System 1
4x − 5y = 2 → eq.1
3x − y = 8 → eq.2

Rearranging both equations:
y = 4/5 x - 2/5 → eq.1
y = 3 x - 8 → eq.2

Graphing both the equations.
Solution set : (x,y)→(3.455,2.634)

Solving System 2
4x − 5y = 2 →eq.1
10x − 7y = 18 →eq.2

Rearranging both equations:
y = 4/5 x - 2/5 → eq.1
y = 10/7 x - 18/10 → eq.2

Graphing both the equations.
Solution set : (x,y)→(3.455,2.634)

Solving System 3
4x − 5y = 2 → eq.1
3x − 8y = 4 →eq.2

Rearranging both equations:
y = 4/5 x - 2/5 → eq.1
y = 3/8 x - 4/8 → eq.2

Graphing both the equations.
Solution set : (x,y)→(-0.235,-0.588)

Solving System 4
4x − 5y = 2 → eq.1
10x + 3y = 15 → eq.2

Rearranging both equations:
y = 4/5 x - 2/5 → eq.1
y = -10/3 x + 5 → eq.2

Graphing both the equations.
Solution set : (x,y)→(1.306,0.645)

Therefore, the best answer choice is:
A. System 1 and system 2, because the second equation in system 2 is obtained by adding the first equation in system 1 to two times the second equation in system 1