Zina solves a system of linear equations by elimination and finds that the solution to a system is (2, 2). One of the equations is

a + b = 4. Which answer could be the other equation?

a + 3b = 4

2a + 2b = 2

4a + 4b = 8

a + 3b = 8

Answer: D. a + 3b = 8

Step-by-step explanation:

We have that one of the equation of the system is a + b = 4 and the solution is given by (a, b) = (2,2).

Now, since the solution is (a, b) = (2,2), then it must satisfy the equations in the options.

So, substituting (2,2) in the options, we get:

A. a + 3b = 4 → a + 3b = 4 → 2 + 3 * 2 = 4 → 2 + 6 = 4 → 8 = 4, which is not true.

B. 2a + 2b = 2 → a + b = 1 → 2 + 2 = 1 → 4 = 1, which is not true.

C. 4a + 4b = 8 → a + b = 2 → 2 + 2 = 2 → 4 = 2, which is not true.

D. a + 3b = 8 → 2 + 3 * 2 = 8 → 2 + 6 = 8 → 8 = 8, which is correct.

So, we get that the other equation of this system is a + 3b = 8.

We can also check using elimination method that these equations give the result (a, b) = (2,2).

a + b = 4

a + 3b = 8

Subtracting both equation gives us,

- 2b = - 4 i. e. b = 2

So, a + b = 4 → a = 4 - b → a = 4 - 2 → a = 2.

Thus solution is (2,2).

Hence, option D is correct.

Step-by-step explanation:

a + 3b = 4

2a + 2b = 2

4a + 4b = 8

a + 3b = 8