Step-by-step explanation:
there are 2 main approaches (in their core they are the same, of course, but they look different) :
1. use one equation to express one variable by the second, and then use this in the second equation to solve for the remaining variable. with that you go back into the first equation and solve for the first variable.
2. multiply both equations by certain factors as needed, then add both results, so that there is one summary equation with only one variable, and then solve for it. then use that in one of the original equations and solve for the second variable.
using 1.
3x + 2y = 1
3x = 1 - 2y
x = (1 - 2y)/3
2x + 7y = 3
2(1 - 2y)/3 + 7y = 3
2(1 - 2y) + 21y = 9
2 - 4y + 21y = 9
17y = 7
y = 7/17
x = (1 - 2y)/3 = (1 - 2×7/17)/3 = (1 - 14/17)/3 =
= (17/17 - 14/17)/3 = 3/17 / 3 = 1/17
using 2.
multiply first equation by 2, the second by -3
6x + 4y = 2
-6x - 21y = -9
----------------------
0 -17y = -7
-17y = -7
17y = 7
y = 7/17
and so on (as under 1.).
