zina solves a system of linear equations by elimination and finds that the solution to a system is (2, 2)…

Explanation:

Step1: Recall the solution

The solution to the system is ((a, b) = (2, 2)). So we need to check which equation is satisfied when (a = 2) and (b = 2).

Step2: Check first option

Substitute (a = 2), (b = 2) into (a + 3b): (2+3\times2=2 + 6=8\neq4). So first option is wrong.

Step3: Check second option

Substitute (a = 2), (b = 2) into (2a + 2b): (2\times2+2\times2 = 4 + 4=8\neq2). So second option is wrong.

Step4: Check third option

Substitute (a = 2), (b = 2) into (4a + 4b): (4\times2+4\times2=8 + 8 = 16\neq8)? Wait, no, wait: (4a + 4b=4(a + b)). Since (a + b=4), then (4\times4 = 16)? Wait, no, the equation is (4a + 4b = 8). Wait, maybe I miscalculated. Wait (a=2), (b = 2): (4\times2+4\times2=8 + 8 = 16), but (16\neq8). Wait, no, wait the third option is (4a + 4b = 8)? Wait, no, wait the original equation given is (a + b = 4). Let's check the fourth option.

Step5: Check fourth option

Substitute (a = 2), (b = 2) into (a + 3b): (2+3\times2=2 + 6 = 8). So (a + 3b = 8) when (a = 2), (b = 2). Wait, let's re - check the third option. Wait (4a+4b = 8) can be simplified by dividing both sides by 4: (a + b=2), but the solution is (a + b = 4), so that's inconsistent. Wait, the fourth option: (a=2), (b = 2): (2+3\times2=8), so (a + 3b = 8) holds. Wait, let's re - check each option:

Option 1: (a + 3b) with (a = 2), (b = 2): (2+6 = 8\neq4).

Option 2: (2a + 2b=4 + 4 = 8\neq2).

Option 3: (4a + 4b=8 + 8 = 16\neq8).

Option 4: (a + 3b=2+6 = 8), which matches the equation (a + 3b = 8).

Answer:

D. (a + 3b = 8) (assuming the options are labeled as A: (a + 3b = 4), B: (2a + 2b = 2), C: (4a + 4b = 8), D: (a + 3b = 8))