Explanation:
that is really easy : you want to multiply one or both of the equations with factors (left and right sides, of course), so that one variable expression is the same in both equations and we can really subtract or add then both equations and then solve only for one variable ...
1.
we multiply the first equation by 3 and then add both equations.
3x + 3y = 6
-3x + 4y = 15
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0 + 7y = 21
7y = 21
y = 3
x + 3 = 2
x = -1
2.
we multiply the first equation by 5 and then add both equations.
5x - 5y = -40
7x + 5y = 16
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12x 0 = -24
12x = -24
x = -2
-2 - y = -8
-y = -6
y = 6
5.
we multiply the first equation by -2 and then add both equations.
-4x - 10y = -22
4x + 3y = 1
-------------------------
0. -7y = -21
-7y = -21
y = 3
4x + 3×3 = 1
4x = -8
x = -2
6.
we multiply the first equation by 2 and then add both equations.
6x - 6y = -12
-5x + 6y = 12
----------------------
x. 0 = 0
x = 0
6y = 12
y = 2
7.
we multiply the first equation by -2 and then add both equations.
-6x - 8y = -58
6x + 5y = 43
------------------------
0 -3y = -15
-3y = -15
y = 5
6x + 5×5 = 43
6x + 25 = 43
6x = 18
x = 3
8.
we multiply the first equation by 5 and the second equation by -3 and then add both equations.
40x + 15y = 20
21x - 15y = 102
---------------------------
61x. 0 = 122
61x = 122
x = 2
40×2 + 15y = 20
80 + 15y = 20
15y = -60
y = -4