Zina solves a system of linear equations by elimination and finds a solution of (2, 2). one of the equations is a + b = 4. what is the other equation?
a. a + 3b = 4
b. 2a + 2b = 2
c. 4a + 4b = 8
d. a + 3b = 8

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.

g

step-by-step explanation:

a

step-by-step explanation: