3x+4y=27,5x-3y=16 elimination using multiplication?

3x + 4y = 27
5x - 3y = 16

3x + 4y = 27
5(3x + 4y) = 5(27)
15x + 20y = 135

5x - 3y = 16
3(5x - 3y) = 3(16)
15x - 9y = 48

....15x + 20y = 135
–) 15x ...- 9y = ..48
-----------------------------------
.............29y = ..87

29y = 87
y = 87/29
y = 3

3x + 4y = 27
3x + 4(3) = 27
3x + 12 = 27
3x = 27 - 12
x = 15/3
x = 5

∴ x = 5 , y = 3

3x+4x =27

9x + 12y = 81
20x - 12y = 64------ADD

29x = 145

x = 5

15 + 4y = 27
4y = 12
y = 3

x = 5 , y = 3

1. 3x + 4y = 27
5x - 3y = 16
Multiply the first equation by 5 and the second equation by -3.
-3(5x-3y) = 16(-3)
15(3x+4y)= 27(5) =
-15x+9y = -48
15x +20y = 81
______________
29y=87
y=3

Then use the first equation and substitute 3 for y
3x+4y = 27
3x + 4(3) = 27
3x +12 = 27
3x = 15
x=5

The solution to the system is (5,3)

One more thing. To check it use the second equation and substitute 5 for x and 3 for y.
5x-3y=16
5(5) - 3(3) =16
25 - 9 = 16
16 = 16 Correct!

x= 5
y= 3