Solving a system of three equations with infinite many solutions

[@davidthaler7018]

You can almost tell how this will turn out just by looking. If you divide all terms in the first equation by 2, the result is a copy of the third equation. Using the two identical equations to eliminate a variable cancels ALL terms to zero, leaving you with a single equation in 3 variables, which has an infinite number of solutions.

[@vandrickinman-benavente1975]

Well, you just saved my GPA by a full 2 points lol

[@rampantfox1]

Your second analysis of why there are infinitely many solutions is not quite correct. You used equations 2 and 3 to eliminate y, but - x - z = 7 alone does not imply infinitely many solutions. If this system had a solution, and you were going to solve it using elimination, you could eliminate y using equations 2 and 3, but you would also have to eliminate y using a different pair of equations. If you were unlucky enough to use equations 1 and 2, you would get a second equation in x and z alone. You would then take your first equation (which you call equation B) and this second equation and solve a 2x2 system. THAT process would yield a 0 = 0 case, and hence infinitely many solutions.

[@alexz4006]

Thats not really solving the system though thats just saying that it has infinite solutions and its dependent

[@Charlie-hv3dh]

Yeah, but in hs algebra 2 they really just want you to say “there’s infinitely many solutions” and that’s that. Scared of how you solve them though-

[@RealShaquilleOneal]

@@Charlie-hv3dhbruh this is on the first test of the year and im only a sophomore so idk if i should drop the class or no

[@nancy-zl8tl]

@@Charlie-hv3dh nah for us we actually have to solve for it [using one variable so for this i think it's (x, 5-x, -6)]

[@Charlie-hv3dh]

ahh alright @@nancy-zl8tl

[@Charlie-hv3dh]

omg a fellow swiftie@@nancy-zl8tl

[@santhoshmedishetty]

Please provide playlist of matrix

[@zxcvbnmaw1]

You don't actually show how to solve this...

[@carlosjoaquinsantos1117]

I got the vlue of x y and z By multiplying the 1st equation by 3 and the 2nd Equation I multiplied it by -2

[@brianmclogan]

there are multiple ways to solve

[@carlosjoaquinsantos1117]

Ah.. thanks

[@carlosjoaquinsantos1117]

I got Y=6; z=0; x= -7

[@brianmclogan]

do not see a mistake in my end

[@michaelangeloelpedes8440]

y really is 6 , but z and x got infinite solution , x+z = -7 , z could be the -7 and x could be 0 , any number is possible as long x = -z - 7 and z = -x - 7

[@sanju.0000]

You could solve it easily with Cramer's Rule

[@carlosjoaquinsantos1117]

I dont know if i am right

[@brianmclogan]

I do not see a mistake on my end

[@hhenry2576]

Not helping

[@KW-gb9cd]

Well, that was a waste of time.

[@iamglued-so9mq]

@@KW-gb9cd Yes if you already knew this. Otherwise you would've been stumped when solving it for the first time