Answer:
None of the systems is equivalent to the given system
Step-by-step explanation:
we have the given system
[tex]x-y=3[/tex] ---> equation A
[tex]x+y=5[/tex] ---> equation B
Solve the system
Adds equation A and equation B
[tex]x-y=3\\x+y=5\\------\\ 2x=8\\x=4[/tex]
Find the value of y
[tex](4)-y=3[/tex] ------> [tex]y=4-3=1[/tex]
The solution of the given system is the point (4,1)
we know that
If a system is equivalent to the given system, then the solution of both systems must be the same
Verify each case
case A) 2x - y = 18 and x + 2y = 10
[tex]2x-y=18[/tex] ---> equation A
[tex]x+2y=10[/tex] ---> equation B
Substitute the value of x and y in both equations and then compare the results
[tex]x=4,y=1[/tex]
equation A
[tex]2(4)-(1)=18[/tex]
[tex]7=18[/tex] ----> is not true
therefore
the system is not equivalent to the given system
case B) 4x - 3y = 18 and x + 2y = 10
[tex]4x-3y=18[/tex] ---> equation A
[tex]x+2y=10[/tex] ---> equation B
Substitute the value of x and y in both equations and then compare the results
[tex]x=4,y=1[/tex]
equation A
[tex]4(4)-3(1)=18[/tex]
[tex]13=18[/tex] ----> is not true
therefore
the system is not equivalent to the given system
case C) 2x - 3y = 3 and x + 2y = 5
[tex]2x-3y=3[/tex] ---> equation A
[tex]x+2y=5[/tex] ---> equation B
Substitute the value of x and y in both equations and then compare the results
[tex]x=4,y=1[/tex]
equation A
[tex]2(4)-3(1)=18[/tex]
[tex]5=18[/tex] ----> is not true
therefore
the system is not equivalent to the given system
