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iiamentertainment
 2 years ago
What is the solution of the system of equations?
{ 2x + 2y + 3z = 6
3x + 5y + 4z = 3
2x + 3y + 4z =  10}
Three equations
iiamentertainment
 2 years ago
What is the solution of the system of equations? { 2x + 2y + 3z = 6 3x + 5y + 4z = 3 2x + 3y + 4z =  10} Three equations

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iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0So 2x + 2y + 3z = 6 2y + 3z = 2x  6 2y = 2x 3z  6 y = 2x 3z  6/2 y = x 3/2z  3 ?

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0@CalebBeavers

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0@abb0t please help ..

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.2Well, you can use 1 of 2 methods. Substitution, or Elimination. Are you familiar with either of them?

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0im familar with substitution

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.2Ah, I almost want to suggest using gausselimination, but that's beyond algebra 2. Well, I think it might be easier to use elimination actually to eliminate one equation first and then a second to get 2variable equations. Does that make sense?

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.2Hint, start by eliminating the x's since equations (1) and (3) both begin with 2. Multiply the first (or second) by 1.

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0Um im not that good with elimination , butf you walk me through and let me solve it i think ill be ok

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.2Yes. I will walk you through it, mate. Start by eliminating one variable in the system of equations. As I said before, It might be easier to eliminate the x from equations (1) and (3) since they both begin with the number 2 [NOTE: Do NOT do anything to eq (2), yet]. You can do this by multiplying either (1) or (3) by 1. Try it and let me know which one you choose and what ur answer is.

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.01(2x + 2y + 3z)= 6 2x  2y  3z = 6 ?

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.2You're 90% correct, when you multiply (1) to the eq, you also have to multiply it to the 6 and you know (1)(6) = 6. making eq(1) 2x2y3z = 6 I'm going to use the term: eq(#) just so I type less :P But notice that eq(1) and eq(2) can be added. And the x' term cancels out nicely. So that you get a new equation with only y's and z's. When you add everything! Including the 6 and 10. Try it.

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.02x + 3y + 4z =  10 2x  2y  3z = 6 y + 1 = 4 y = 5 ?

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.2i have to step out for a moment, but I will tell you the next few steps. Next, do the same thing to eliminate x! from eq(2)! To get a second equation with only y's and z's! Notice that now you have TWO system of equations which you can use elimination (again) or substitution (which you said you like) to solve for either y or z! Once you have your y or z value, plug it back into the original 2 system equation to solve for either y or z (which ever variable you chose to solve for). Once you solved for the 2nd variable you should have TWO variables: y AND z! Now plug in everything into ANY of the equations of the 3systems and solve for x! You can check by plugging everything in and you should get either 6, 3, or 10! If you are correct, you should get those answers!

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0@blondie16 can you help , im confused

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2You are certainly on the right track. You seem to have forgotten the 'z' variable when adding "4z" and "3z". This gives you a z. So your equation becomes: y + z = 4

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0Ok thats what i did wrong ok cool, then what

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2What @abb0t suggested next was to use elimination once more. This time with eq(1) and eq(2). The focus here is to, again, eliminate the 'x' variable. equation 1: 2x + 2y + 3z = 6 equation 2: 3x + 5y + 4z = 3 If you multiply eq(1) by 3/2 you will be able to then add it to eq(2) to cancel out the 'x' again. What do you obtain when you multiply eq(1) through by 3/2 ?

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.03/2(2x + 2y + 3z) = 6 3x  3y  4.5z = 9 3x + 5y + 4z = 3 2y .5z = 6 ?

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0@LogicalApple

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2The 9 + 3 should be a 12 so 2y  0.5z = 12

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0i thoue were subtractingnot adding

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.23x + 3x = 0 3y + 5y = 2y 4.5z + 4z = 0.5z 9 + 3 = 12 You added everything else correctly but the last numbers

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0Oh Ok , Next Step?

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2In any event you are now down to a system of 2 equations with 2 variables y + z = 4 2y  0.5z = 12 You can use substitution at this point.

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2Notice how the elimination method eliminates one of the variables, leaving you with only two to deal with. From here you could set y = 4  z in the first equation and substitute this value of y into the second equation and solve for z

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.02x + 2(4 z) + 3z = 6 like that

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2No, I meant the second equation listed here: y + z = 4 2y  0.5z = 12 Not any of the original equations

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.02(4 z)  0.5z = 12 8  2z  .5z = 12 8 + 3z = 12 3z = 20 z = 6.67

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.22z  0.5z = 2.5z So you should have 8  2.5z = 12

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.08  2.5z = 12 2.5z = 20 z = 8

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2And we know: y + z = 4

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0y + (8) = 4 y = 4

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.0@LogicalApple

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2Yes, that is also correct. Now you know what y and z are. Use these values in any one of the original three equations and you will obtain the value for x.

iiamentertainment
 2 years ago
Best ResponseYou've already chosen the best response.02x + 2(4) + 3(8) = 6 2x + 8  24 = 6 2x  16 = 6 2x = 10 x = 5 y = 4 z = 8 @LogicalApple

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2Fantastic. (5, 4, 8) is the correct solution

biasophia
 10 months ago
Best ResponseYou've already chosen the best response.0solve the system of equations by elimination 3x+y+2z=3 2x3yz=3 x+2y+z=4
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