Question

x - y = 3 x + y = 5 Which of the following systems is equivalent to the given system? 2x - y = 18 and x + 2y = 10 4x - 3y = 18 and x + 2y = 10 2x - 3y = 3 and x + 2y = 5

Answer 1

Answer:

None of the systems is equivalent to the given system

Step-by-step explanation:

we have the given system

$x-y=3$ ---> equation A

$x+y=5$ ---> equation B

Solve the system

Adds equation A and equation B

$x-y=3\\x+y=5\\------\\ 2x=8\\x=4$

Find the value of y

$(4)-y=3$ ------> $y=4-3=1$

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

$2x-y=18$ ---> equation A

$x+2y=10$ ---> equation B

Substitute the value of x and y in both equations and then compare the results

$x=4,y=1$

equation A

$2(4)-(1)=18$

$7=18$ ----> is not true

therefore

the system is not equivalent to the given system

case B) 4x - 3y = 18 and x + 2y = 10

$4x-3y=18$ ---> equation A

$x+2y=10$ ---> equation B

Substitute the value of x and y in both equations and then compare the results

$x=4,y=1$

equation A

$4(4)-3(1)=18$

$13=18$ ----> is not true

therefore

the system is not equivalent to the given system

case C) 2x - 3y = 3 and x + 2y = 5

$2x-3y=3$ ---> equation A

$x+2y=5$ ---> equation B

Substitute the value of x and y in both equations and then compare the results

$x=4,y=1$

equation A

$2(4)-3(1)=18$

$5=18$ ----> is not true

therefore

the system is not equivalent to the given system