Question

Which ordered pair (a,b) is a solution to the given system ?
2a-5b=1
3a+5b=14

Answer 1

2a - 5b = 1
3a + 5b = 14
-----------------------add
5a = 15
a = 3

2(3) - 5b = 1
6 - 5b = 1
5b = 5
b = 1

answer
(3, 1 ) is a solution

Answer 2

(3, 1)

Explanation:

Given system of equation,

2a - 5b = 1 ----(1),

3a + 5b = 14 -----(2)

Adding equation (1) and (2),

We get,

5a = 15

⇒ a =
`(15)/(5)` = 3

Now, from equation (1),

2(3) - 5b = 1

6 - 5b = 1

- 5b = 1 - 6

-5b = -5

⇒ b =
`(-5)/(-5)` = 1

Hence, the solution of the given system of equations is ( 3, 1).