This one just looks confusing af. Could you maybe work out one and I work out the other?
These are difficult....and often lengthy......the other problem is that there is no "set" way to proceed.....[P.S.....watch your math carefully....one mistake dooms you !!! ]
I'll do the first one just to demonstrate...
2a + 3b - 5c = -5 (1)
-2a - 2b - c = -14 (2)
4a - 4b + 4c = -4 divide this equation by 2 ⇒ 2a - 2b + 2c = -2 (3)
Add (1) and (2) Add (2) and (3)
2a + 3b - 5c = -5 -2a - 2b - c = -14
-2a - 2b - c = -14 2a - 2b + 2c = -2
________________ _________________
b - 6c = -19 (4) -4b + c = -16 ⇒ c = 4b - 16 (5)
Sub (5) into ( 4) and we have
b - 6(4b - 16) = -19
b - 24b + 96 = -19
-23b + 96 = -19 subtract 96 from both sides
-23b = -115 divide both sides by -23
b = 5
Use (5) to find c
c = 4(5) - 16 = 20 - 16 = 4
And using (3) to find "a" we have
2a - 2(5) + 2(4) = -2
2a - 10 + 8 = -2
2a -2 = -2 add 2 to both sides
2a = 0 ⇒ a = 0
RP...this requires a bit of experience to master...I would stick to solving equations in two variables and make sure you felt comfortable with that before you attmpted these.....just my opinion....
As a disclaimer...I can show you something known as "Cramer's Rule" where no solving is involved...however...it's also a little lengthy...but not difficult...!!!!!
But I have to do these now. Am I supposed to get c as well? I attempted #10 but I didn't do it well lol so I just erased everything. Dang it I have to go soon but want to get this done today!
10)
2a - 4b - 2c = -4 divide by 2 ⇒ a - 2b - c = -2 (1)
-3a + 3b +6c = 30 divide by 3 ⇒ - a + b + 2c = 10 (2)
-a - 3b + c = 17 -a - 3b + c = 17 (3)
Add (1) and (2) Add (1) and (3)
a - 2b - c = -2 -a - 2b - c = -2
-a + b + 2c = 10 a -3b + c = 17
________________ ______________
-b + c = 8 ..so.. -5b = 15
c = 8 + b (4) b = -3 (5)
Sub (5) into (4)
c = 8 + (-3)
c = 5
And using (1) to find a
a - 2b - c = -2
a - 2(-3) - (5) = -2
a + 6 - 5 = -2
a + 1 = -2
a = -3