x + y + z = 11

x + y + z = 11

0.70x + 0.55y + 0.50z = 6.70

x = 3z

\(\begin{array}{lrcrcrcr} (1) & x &+& y &+& z &=& 11 \\ (2) & 0.70x &+& 0.55y &+& 0.50z &=& 6.70 \\ \\ \hline \\ x= 3z: \\ \\ (1) & 3z &+& y &+& z &=& 11 \\ (2) & 0.70\cdot (3z) &+& 0.55y &+& 0.50z &=& 6.70 \\ \\ \hline \\ (1) & && y &+& 4z &=& 11 \\ (2) & 2.1\cdot z &+& 0.55y &+& 0.50z &=& 6.70 \\ \\ \hline \\ (1) & && y &+& 4z &=& 11 \\ (2) & && 0.55y &+& 2.60z &=& 6.70 \\ \\ \hline \\ (1) & && y && &=& 11 - 4z\\ (2) & && 0.55y &+& 2.60z &=& 6.70 \\ & && 0.55(11 - 4z) &+& 2.60z &=& 6.70 \\ & && 0.55\cdot 11 - 0.55\cdot 4z &+& 2.60z &=& 6.70 \\ & && 6.05 - 2.20z &+& 2.60z &=& 6.70 \\ & && 6.05 &+& 0.40z &=& 6.70 \\ & && && 0.40z &=& 6.70 -6.05 \\ & && && 0.40z &=& 0.65 \\ & && && z &=& \frac{0.65} {0.40}\\ & && && \mathbf{z} &\mathbf{=}& \mathbf{ 1.625 }\\ \\ \hline \\ (1) & && y && &=& 11 - 4z\\ & && y && &=& 11 - 4\cdot 1.625\\ & && y && &=& 11 - 6.5\\ & && \mathbf{y} && &\mathbf{=}& \mathbf{ 4.5 }\\ \\ \hline \\ x= 3z \\ x = 3\cdot 1.625\\ \mathbf{x = 4.875}\\ \end{array}\)

x + y + z = 11

0.70x + 0.55y + 0.50z = 6.70

x = 3z

Solve the following system:
{y+4 z = 11 |     (equation 1)
0.55 y+2.6 z = 6.7 |     (equation 2)
Subtract 0.65 × (equation 1) from equation 2:
{4 z+y = 11 |     (equation 1)
0 z-0.1 y = -0.45 |     (equation 2)
Divide equation 2 by -1.:
{4 z+y = 11 |     (equation 1)
0 z+0.1 y = 0.45 |     (equation 2)
Divide equation 2 by 0.1:
{4 z+y = 11 |     (equation 1)
0. z+y = 4.5 |     (equation 2)
Subtract equation 2 from equation 1:
{4 z+0 y = 6.5 |     (equation 1)
0 z+y = 4.5 |     (equation 2)
Divide equation 1 by 4:
{z+0 y = 1.625 |     (equation 1)
0 z+y = 4.5 |     (equation 2)
Collect results:
Answer: | 
| {z = 1.625
y = 4.5

x=1.625 X 3=4.875