a:
a + 2 x b + 3 x c = 19
a + 2 x b + 3 x c + −2 x b = 19 + −2 x b
a + 3 x c = −2 x b + 19
a + 3 x c + −3 x c = −2 x b + 19 + −3 x c
a = − 2 x b − 3 x c + 19
Just continue like this now you just have to plug them in and then solve for each one until you get a solid answer for one variable and then plug them in to find the rest.