Question

If 2a+3b=17 and a +2b = 7, then (3a+5b)÷2 =

If you could explain, that’d be great!

Answer 1

12

Explanation:

Use the first two equations to solve for a and b.

multiply the second equation all the way through by -2

(-2)(a + 2b) = (-2)(7)

-2a -4b = -14 Add this to the first equation.

-2a - 4b = -14

+ 2a + 3b = 17

-b = 3 Multiply both sides by -1

b = -3 Plug -3 back into either of the 2 original equations to find a

a + 2b = 7

a + 2(-3) = 7

a - 6 = 7 Add 6 to both sides

a = 13

Now that we know a = -3 and b = 13, we can plug that into the third equation:

`((3a + 5b))/(2)`

`(3(13) + 5(-3))/(2))`

`(39 -15)/(2)`

`(24)/(2)` = 12