Solve the system of equations using the addition method.
-$$\begin{array} { l }
- 0.2 x + 0.3 y - 0.3 z = - 2.8 \
0.4 x - 0.1 y + 0.2 z = 2 \
- 0.2 x - 0.4 y + 0.4 z = 2.8
\end{array}$$
A)(2, -4, 4)
B)(-0.6, 8, 5)
C)(-0.6, 10, 4)
D)(-0.4, 10, 5)

Question

Solve the system of equations using the addition method.
-$$\begin{array} { l } 
- 0.2 x + 0.3 y - 0.3 z = - 2.8 \
0.4 x - 0.1 y + 0.2 z = 2 \
- 0.2 x - 0.4 y + 0.4 z = 2.8
\end{array}$$
A)(2, -4, 4)
B)(-0.6, 8, 5)
C)(-0.6, 10, 4)
D)(-0.4, 10, 5)

Quizplus · Accepted Answer

Explanation:Add the first and third equations to eliminate x:-0.4x + 0.1y + 0.1z = 0Add the second and third equations to eliminate x:0.2x - 0.5y + 0.6z = 4.8Solve the system of two equations in two variables:0.1y + 0.1z = 0-0.5y + 0.6z = 4.8Multiply the first equation by 5 to get:0.5y + 0.5z = 0Add this to the second equation to get:0.6z = 4.8Divide both sides by 0.6 to get:z = 8Substitute this back into the first equation to get:0.1y + 0.1(8) = 00.1y + 0.8 = 0Subtract 0.8 from both sides to get:0.1y = -0.8Divide both sides by 0.1 to get:y = -8Substitute z = 8 and y = -8 back into the first equation to get:-0.2x + 0.3(-8) - 0.3(8) = -2.8-0.2x - 2.4 - 2.4 = -2.8-0.2x = 2.8Divide both sides by -0.2 to get:x = -14Therefore, the solution to the system of equations is x = -14, y = -8, and z = 8.