Simultaneous linear equations

solve:

1.
3x + y = 23
6x + y = 44

2.
4x - 3y = 21
2x + 3y = 33

3.
5x + 2y = 13
6y + 5x = 29

4.
5x - 4y = 2
10x - 4y = 32

5.
2x + 7y = 48
x + 3y = 21

6.
8x - 3y = 44
2y - 4x = -20

1) 3x + y = 23
6x + y = 44

Subtract 1st from 2nd, 
3x = 21
x = 7
Then, y = 23 - 3(7) = 2

In short, Your Answer would be: (7, 2)

2) 4x - 3y = 21
2x + 3y = 33

Add the equations, 
6x = 54
x = 9
Then, 2(9) + 3y = 33
3y = 33 - 18
y = 15/3
y = 5

In short, Your Answer would be: (9, 5)

3) 5x + 2y = 13
6y + 5x = 29
Subtract 1st from 2nd equation, 

4y = 16
y = 4
Then, 5x  = 13 - 2(4)
x = 5/5 = 1

In short, Your Answer would be: (1, 4)

4)  5x - 4y = 2
10x - 4y = 32
Subtract 1st from 2nd equation, 
5x = 30
x = 6

Then, 5(6) - 2 = 4y
y = 28/4 = 7

In short, Your Answer would be: (6, 7)

5) 2x + 7y = 48
x + 3y = 21

Here, x = 21-3y
Substitute in in 1st equation, 
2(21-3y) + 7y = 48
42 - 6y + 7y = 48
y = 6

Then, x = 21 - 3(6) = 3

In short, Your Answer would be: (3, 6)

6) 8x - 3y = 44
2y - 4x = -20

Multiply 2nd equation by 2 
-8x + 4y = -40
Now, add it to 1st equation, 
y = 4

Then, 2(4) - 4x = -20
4x = 8 + 20
x = 28/4 = 7

In short, Your Answer would be: (7, 4)

Hope this helps!

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