Question

Consider the following system of equations. x+y=11 and 2x - 3y=-3. Which equation can be added to the system so that the solution does not change.
A) x-y=2
B) -2x+2y=-2
C)3x+y=20
D)x+2y=18​

Answer 1

Answer:

B) -2x+2y=-2

Step-by-step explanation:

we have

$x+y=11$ ----> equation A

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

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (6,5)

see the attached figure

Remember that

If a equation is added to the system so that the solution does not change, then the solution of the system must be a solution of the equation added

Verify each case

The solution of the system is (6,5)

substitute the value of x and the value of y in each equation

case A) x-y=2

6-5=2

1=2 ----> is not true

therefore

This equation can't be added to the system

case B) -2x+2y=-2

-2(6)+2(5)=-2

-12+10=-2

-2=-2 ----> is true

therefore

This equation can be added to the system

case C) 3x+y=20

3(6)+5=20

18+5=20

23=20 ----> is not true

therefore

This equation can't be added to the system

case D) x+2y=18​

5+2(6)=18

5+12=18

17=18 ----> is not true

therefore

This equation can't be added to the system