The weights W1 and W2 exerted on each rafter for the roof...

The weights $W_{1}$ and $W_{2}$ exerted on each rafter for the roof truss shown in the figure are determined by the system of linear equations. Solve the system.
(FIGURE CAN'T COPY)
$$\begin{aligned}W_{1}+\sqrt{2} W_{2} &=300 \\\sqrt{3} W_{1}-\sqrt{2} W_{2} &=0\end{aligned}$$

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Key Concepts

System of Linear Equations

A system of linear equations is a set of equations where each equation is linear in the unknowns. Solving such a system involves finding values for the variables that satisfy every equation simultaneously. In the context of this problem, the equations are used to model forces acting on a roof truss, and the solution represents the weights acting on different components.

Solving Methods (Substitution/Elimination)

There are several methods for solving systems of linear equations, including substitution and elimination. The substitution method involves solving one of the equations for one variable and then substituting that expression into another equation. The elimination method involves adding or subtracting the equations to cancel one of the variables. In this problem, these methods are applicable even in the presence of irrational coefficients.

Irrational Coefficients

Equations with irrational coefficients, such as those involving square roots, require careful algebraic manipulation. Despite the presence of irrational numbers, the common techniques for solving linear systems remain valid. The operations of addition, subtraction, multiplication, and division are used to isolate the variables, just as in equations with rational coefficients.

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