Question

Which ordered pair (a, b) is the solution to the given system?

2a-5b=1
3a+5b=14
(1, 3)
(3, 1)
(29/5,15)
15,29/5

Answer 1

b

Explanation:

Answer 2

2a - 5b = 1

3a + 5b = 14

Let's solve this system using elimination. Add the equations together to cancel the b-terms, then solve for a.

2a - 5b = 1

3a + 5b = 14

+___________

5a - 0 = 15

5a = 15

a = 3

Next, plug 3 for a into either of the equations and solve for b.

2a - 5b = 1

2(3) - 5b = 1

6 - 5b = 1

- 5b = -5

b = 1

Lastly, check all work by plugging both values for their respective variables.

2a - 5b = 1

2(3) - 5(1) = 1

6 - 5 = 1 -- This is true

3a + 5b = 14

3(3) + 5(1) = 14

9 + 5 = 14 -- This is true

The solution to the system of equations is (3, 1).

Explanation: