Question

Line Q is represented by the following equation: 2x + y = 11

Which equation completes the system that is satisfied by the solution (3, 5)?

x + 2y = 15
x + y = 15
x + y = 8
x − y = 2

Answer 1

hello : the system is :
2x + y = 11
x+y =8
because 2(3)+5=11 and: 3+5 = 8

Answer 2

Option C.

Explanation:

Equation of line Q is

`2x+y=11`

We need to find the equation which complete the system that is satisfied by the solution (3,5).

It means the equation of line must be true for (3,5).

First equation is,

`x+2y=15`

Check the equation for (3,5).

`(3)+2(5)=3+10=13\\eq 15`

It means option A is incorrect.

Similarly check the oher options.

`x+y=15\Rightarrow (3)+(5)=8\\eq 15`

`x+y=8\Rightarrow (3)+(5)=8`

`x-y=2\Rightarrow (3)-(5)=-2\\eq 2`

Only equation
`x+y=8` is true for (3,5).

Hence the correct option is C.