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505-555 (Easy)|   Algebra|      
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Bunuel
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x + 2y + 3z = 4 and 5x + 4y + 3z = 8. What is the value of x + y + z? 18 Mar 2023, 13:00
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82% (01:46) correct 18% (03:00) wrong based on 249 sessions

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If \(x + 2y + 3z = 4\) and \(5x + 4y + 3z = 8\). What is the value of \(x + y + z\)?

A. 1

B. 2

C. 3

D. 4

E. 5
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SusantKumarNand
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x + 2y + 3z = 4 and 5x + 4y + 3z = 8. What is the value of x + y + z? 19 Mar 2023, 19:26
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X+ 2y + 3 Z = 4 , and 5X + 4X + 3Z = 8
Adding both the equation
6x + 6y+ 6 z = 12
X+y+z= 2

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Rabab36
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x + 2y + 3z = 4 and 5x + 4y + 3z = 8. What is the value of x + y + z? 19 Mar 2023, 10:40
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x+2y+3z=4------1
5x+4y+3z=8-------2

eq 2-1
we get
2x+y=2----------3
now
5*equation1 -equation 2
we get y +2z=2---------4

eq 4+3
we get x+y+z=2

option B correct
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x + 2y + 3z = 4 and 5x + 4y + 3z = 8. What is the value of x + y + z? 19 Mar 2023, 18:29
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A few ways to solve this:

1. Elimination:

\(x+2y+3z=4\\
5x+4y+3z=8\)

eliminate z

\(4x+2y=4\\
=2x+y=2\\
=y=2-2x\)
not very useful by itself, so next we try to eliminate y

\(5x++4y+3z=8\\
2x+4y+6z=8\)

=

\(3x-6z=0\\
3x=6z\\
x=2z\)
useful, let's plug this in to the original equation and see what happens


now we can replace the x in the original equation
\(x+2y+3z=4\\
(2z)+2y+3z=4\\
2y+5z=4\)

now since \(y=2-2x=2-2(2z)=2-4z\)

replace y

\(2(2-4z)+5z=4\\
4-8z+5z=4\\
-3z=0\\
z=0\)

and since
\(x=2z\\
x=0\)

if both x and z = 0

\(x+2y+3z=4\\
0+2y+0=4\\
2y=4\\
y=2\)

so \(x+y+z=0+2+0=2\)

method 2: try to find the entire equation without eliminating down to 1 variable (might be faster)

We have the equation
\(x+2y+3z=4\\
5x+4y+3z=8\)

the equation lines up nicely that there is a value 3z, let's work on that and see where it takes us

so
\(5x+4y+3z=8\\
minus\\
x+2y+3z=4\\
=\\
4x+2y=4\\
2x+y=2\\
\)

we need to find some version of y+2z to add them together to 2x+2y+2z=something

lets look at the original equation again
\(x+2y+3z=4\\
5x+4y+3z=8\)

We'll need to remove x to form some form of y+z, let's see if this is possible
take the first equation, multiply by 5
\(5x+10y+15z=20\\
minus\\
5x+4y+3z=8\\
=\\
6y+12z=12\\
=\\
y+2z=2\)

perfect! (Sometimes things don't work out this perfectly and we'll have to eliminate 1 by 1)

we have
\(2x+y=2\\
and\\
y+2z=2\)

add these together

\(2x+2y+2z=4\\
x+y+z=2\)

Both ways of solving are okay, the elimination may take longer on these perfectly lined up problems. But the short-cut cannot always be used. More method = more chance to get it right on gmat. Learn both if possible.

Option B
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x + 2y + 3z = 4 and 5x + 4y + 3z = 8. What is the value of x + y + z? 30 Nov 2025, 09:27
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