Question

Please help!!!! ive been trying to get help for almost 2 days and I have yet to get an actual answer :(. Please try to show some work if you can, thank youu​

Answer 1

49.
`x = (1)/(a)` and
`y = 3`

50.
`x = (1)/(2a)` and
`y = (1)/(b)`

Explanation:

We are going to solve these systems of equations using the elimination method.

49. Given:

`5ax + 4y = 17` (1)

`\:\:ax + 7y = 22` (2)

Multiply Eqn(1) by 7 and multiply Eqn(2) by -4 to get

`\:\:35ax + 28y = 119`

`-4ax - 28y = -88`

Adding the two equations above, we get

`31ax = 31 \Rightarrow x = (1)/(a)`

Substituting this value for a into Eqn(2), we get

`y = 3`

50. Given:

`4ax + \:\:by = 3` (3)

`6ax + 5by = 8` (4)

Multiplying Eqn(3) by -5, we get

`-20ax - 5by = -15`

`\:\:\:\:\:\:6ax + 5by = \:\:8`

Adding the two equations above, we get

`-14ax = -7 \Rightarrow x = (1)/(2a)`

Plugging in the value of x into Eqn(3), we get the value for y as

`4a((1)/(2a)) + by = 3`

or

`2 + by = 3 \Rightarrow y = (1)/(b)`