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

x+y=8
this is because

x=3 y=5

3+5=8

Answer 2

Option (c) is correct.

The other equation of system is x+ y = 8

Explanation:

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

We have to find an equation completes the system that is satisfied by the solution (3, 5) .

Since, given (3,5) satisfies the system of equations.

So, (3,5) must satisfies both equation of systems.

For other equation

Put x = 3 and y = 5 i each and check which satisfies the equation.

1) x + 2y = 15

LHS = 3 + 2(5) = 3 + 10 = 13 ≠ RHS.

2) x+ y = 15

LHS = 3 + 5 = 8 ≠ RHS.

3) x + y = 8

LHS = 3 + 5 = 8 = RHS.

4) x - y = 2

LHS = 3 - 5 = -2 ≠ RHS.

Thus, Only equation (3) satisfies the point (3,5).

Thus, The other equation is x+ y = 8