Solve the System to Find $W _ { 1 } \text { and } W _ { 2 }$

Multiple Choice

Solve the system to find $W _ { 1 } \text { and } W _ { 2 }$
-Linear systems occur in the design of roof trusses for new homes and buildings. The simplest type of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If a force of 101 pounds is applied at the peak of the truss, then the forces or weights $W _ { 1 }$ and $W _ { 2 }$ exerted parallel to each rafter of the truss are determined by the following linear system of equations.


$$\frac { \sqrt { 3 } } { 2 } \left( W _ { 1 } + W _ { 2 } \right) = 101$$
$$W _ { 1 } - W _ { 2 } = 0$$

A) $\mathrm { W } _ { 1 } = 33.67 \mathrm { lb } ; \mathrm { W } _ { 2 } = 33.67 \mathrm { lb }$
B) $\mathrm { W } _ { 1 } = 58.31 \mathrm { lb } ; \mathrm { W } _ { 2 } = 50.5 \mathrm { lb }$
C) $W _ { 1 } = 58.31 \mathrm { lb } ; W _ { 2 } = 58.31 \mathrm { lb }$
D) $W _ { 1 } = - 58.31 \mathrm { lb } ; W _ { 2 } = - 58.31 \mathrm { lb }$