Question

1. determine if (5, -2) is a solution to \

$$\begin{cases} -5x + 3y = -31 \\\\ -2x - 5y = 0 \\end{cases}$$

. show all your work.

Explanation:

Step1: Substitute \(x = 5\), \(y=-2\) into first equation

Substitute into \(-5x + 3y=-31\). Left - hand side (LHS) \(=-5\times5+3\times(-2)=-25 - 6=-31\). Right - hand side (RHS) \(=-31\). Since \(LHS = RHS\), the point satisfies the first equation.

Step2: Substitute \(x = 5\), \(y = - 2\) into second equation

Substitute into \(-2x-5y = 0\). LHS\(=-2\times5-5\times(-2)=-10 + 10 = 0\). RHS\(=0\). Since \(LHS=RHS\), the point satisfies the second equation.

Answer:

Since \((5,-2)\) satisfies both equations of the system, \((5,-2)\) is a solution to the system \(

$$\begin{cases}-5x + 3y=-31\\-2x-5y = 0\end{cases}$$

\)