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avatar+681 

\(a+b+c+d=88 \)

\(a+b+c+e=84\)

\(a+b+d+e=82\)

\(a+c+d+e=78\)

\(b+c+d+e=72\)

 Sep 6, 2019

Best Answer 

 #1
avatar+23893 
+3

For the following system of equations, what is the value of c?
\(a+b+c+d = 88 \\ a+b+c+e = 84 \\ a+b+d+e = 82 \\ a+c+d+e = 78 \\ b+c+d+e = 72 \)

 

\(\begin{array}{|lrcll|} \hline (1) & a+b+c+d = 88 \\ (2) & a+b+c+e = 84 \\ (3) & a+b+d+e = 82 \\ (4) & a+c+d+e = 78 \\ (5) & b+c+d+e = 72 \\ \hline (1)+(2)+(3)+(4)+(5): & 4a+4b+4c+4d+4e &=& 88 + 84+82+78+72 \\ & 4(a+b+c+d+e) &=& 404 \quad | \quad : 4 \\ (6) & \mathbf{ a+b+c+d+e } &=& \mathbf{101} \\ \hline (6)-(3): & (a+b+c+d+e)-(a+b+d+e) &=& 101 - 82 \\ & \mathbf{c} &=& \mathbf{19} \\ \hline \end{array}\)

 

laugh

 Sep 6, 2019
edited by heureka  Sep 6, 2019
 #1
avatar+23893 
+3
Best Answer

For the following system of equations, what is the value of c?
\(a+b+c+d = 88 \\ a+b+c+e = 84 \\ a+b+d+e = 82 \\ a+c+d+e = 78 \\ b+c+d+e = 72 \)

 

\(\begin{array}{|lrcll|} \hline (1) & a+b+c+d = 88 \\ (2) & a+b+c+e = 84 \\ (3) & a+b+d+e = 82 \\ (4) & a+c+d+e = 78 \\ (5) & b+c+d+e = 72 \\ \hline (1)+(2)+(3)+(4)+(5): & 4a+4b+4c+4d+4e &=& 88 + 84+82+78+72 \\ & 4(a+b+c+d+e) &=& 404 \quad | \quad : 4 \\ (6) & \mathbf{ a+b+c+d+e } &=& \mathbf{101} \\ \hline (6)-(3): & (a+b+c+d+e)-(a+b+d+e) &=& 101 - 82 \\ & \mathbf{c} &=& \mathbf{19} \\ \hline \end{array}\)

 

laugh

heureka Sep 6, 2019
edited by heureka  Sep 6, 2019
 #2
avatar+681 
+2

thank you so much! =)

Nirvana  Sep 6, 2019

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