Solve the system of linear equations. $$\left\{ \begin{array} { l }
x + y + z = 0 \
3 x + 5 y + 4 z = 9 \
3 x + 6 y + 5 z = 6
\end{array} \right.$$
A) $( 3,12 , - 15 )$
B) $( 3,12,15 )$
C) $( - 3 , - 12 , - 15 )$
D) $( 3 , - 12 , - 15 )$
E) $( - 3,12 , - 15 )$

Question

Solve the system of linear equations.   $$\left\{ \begin{array} { l } 
x + y + z = 0 \
3 x + 5 y + 4 z = 9 \
3 x + 6 y + 5 z = 6
\end{array} \right.$$  
A)  $( 3,12 , - 15 )$
B)  $( 3,12,15 )$
C)  $( - 3 , - 12 , - 15 )$
D)  $( 3 , - 12 , - 15 )$
E)  $( - 3,12 , - 15 )$

Quizplus · Accepted Answer

Explanation:Subtract the first equation from the second and third equations to get2x + 4y + 3z = 92x + 5y + 4z = 6Subtract the second equation from the first equation to get-y - z = -3Solve this equation for z:z = y - 3Substitute this expression for z into the second equation:2x + 5y + 4(y - 3) = 6Simplify:2x + 9y - 12 = 6Subtract 6 from both sides:2x + 9y = 18Divide both sides by 2:x + 9/2y = 9Solve this equation for x:x = 9 - 9/2ySubstitute this expression for x into the first equation:(9 - 9/2y) + y + (y - 3) = 0Simplify:9/2y + 3/2y = 3Multiply both sides by 2/3:y = 2Substitute this value of y into the expression for x:x = 9 - 9/2(2) = 3Substitute the values of x and y into the expression for z:z = 2 - 3 = -1Therefore, the solution to the system of equations is (x, y, z) = (3, 2, -1).

Solve the System of Linear Equations {x+y+z=03x+5y+4z=93x+6y+5z=6\left\{ \begin{array} { l } x + y + z = 0 \\3 x + 5 y + 4 z = 9 \\3 x + 6 y + 5 z = 6\end{array} \right.⎩⎨⎧​x+y+z=03x+5y+4z=93x+6y+5z=6​

Solve the System of Linear Equations $\left\{ \begin{array} { l } x + y + z = 0 \\3 x + 5 y + 4 z = 9 \\3 x + 6 y + 5 z = 6\end{array} \right.$