simulaneous equation help please!?

Question

3x + 2y = 15
2x - 3y = 9

how do you solve this question using algebra simultaneous equations.

Answer 1

1) 3x + 2y = 15
2) 2x - 3y = 9

There are various ways to solve systems - examining the equations can lead you to the best approach

I would use 'elimination' for this one - multiply equation 1 by 3 and equation 2 by 2 so adding the resulting equations eliminates y

1a) 9x + 6y = 45
2a) 4x - 6y = 18

9x + 4x + 6y - 6y = 45 + 18
13x = 63
x = 63/13

Use either eq 1 or 2 to solve for y

1) 3(63/13) + 2y = 15
2y = 15 - 189/13
2y = 195/13 - 189/13
2y = 6/13
y = 3/13

Check
2) 2(63/13) - 3(3/13) = 9
126/13 - 9/13 = 9
117/13 = 9
9 = 9

Answer 2

Find y:
3x + 2y = 15
2y = 15 - 3x
y = 15/2 - 3/2x

Finding x (plug y with 15/2 - 3/2x):
2x - 3(15/2 - 3/2x) = 9
2x - 45/2 + 9/2x = 9
4/2x + 9/2x = 18/2 + 45/2
13/2x = 63/2
x = 63/13

Finding y (plug x with 63/13):
y = 15/2 - 3/2(63/13)
y = 195/26 - 189/26
y = 3/13

Answer: x = 63/13, y = 3/13

Proof (plug x with 63/13, y with 3/13):
3(63/13) + 2(3/13) = 15
189/13 + 6/13 = 15
195/13 = 15
15 = 15

2(63/13) - 3(3/13) = 9
126/13 - 9/13 = 9
117/13 = 9
9 = 9

Answer 3

If you multiply the top equation by 3 and the bottom equation by 2 and then add them up, you get:

9x + 6y = 45
4x - 6y = 18
-----------------
13x = 63
x = 63/13.

You can then substitute the value for x into either equation to solve for y. So in this case, substituting into the bottom equation:

2 * (63/13) - 3y = 9.
126/13 - 3y = 9.
126/13 - 3y = 117/13.
-3y = -9/13.
y = 3/13.

Answer 4

9x + 6y = 45
4x - 6y = 18-----ADD
13x = 63
x = 63/13

189/13 + 2y = 15
2y = 195/13 - 189/13
2y = 6/13
y = 3/13

x = 63 / 13 , y = 3 / 13