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Lena [83]
3 years ago
9

Hello! I'm having a really hard time solving this by Elimination and could really use some help ​

Mathematics
1 answer:
Mamont248 [21]3 years ago
6 0

Answer:

x= 3, y=0, z= 1

Step-by-step explanation:

Let's label the 3 given equations first.

2x +3y +4z= 10 -----(1)

3x +2y -4z= 5 -----(2)

x +4y +2z= 5 -----(3)

(1) +(2):

<em>This</em><em> </em><em>is</em><em> </em><em>to</em><em> </em><em>eliminate</em><em> </em><em>the</em><em> </em><em>z</em><em> </em><em>term</em><em>.</em>

2x +3y +4z +3x +2y -4z= 10 +5

5x +5y= 15

<em>Divide</em><em> </em><em>by</em><em> </em><em>5</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>:</em>

x +y= 3 -----(4)

(3) ×2:

2x +8y +4z= 10 -----(5)

(2) +(5):

<em>This</em><em> </em><em>is</em><em> </em><em>to</em><em> </em><em>eliminate</em><em> </em><em>z</em><em> </em><em>term</em><em>.</em>

3x +2y -4z + 2x +8y +4z= 5 +10

5x +10y= 15

<em>Divide</em><em> </em><em>by</em><em> </em><em>5</em><em> </em><em>throughout</em><em>.</em>

x +2y= 3 -----(6)

(6) -(4):

x +2y -(x +y)= 3 -3

x +2y -x -y= 0

y= 0

subst. y=0 into (4):

x +0= 3

x= 3

subst. x=3, y=0 into (3):

3 +4(0) +2z= 5

3 +2z= 5

2z= 5 -3

2z= 2

z= 2÷2

z= 1

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