Which system of equations has a solution of approximately \( (0.6,-0.8) \) ? \( \begin{array}{l}x+2 y=-1 \text { and } 3 x+y=1 \\ \begin{array}{c}x-2 y=1 \text { and } 3 x+y=1 \\ x-2 y=1 \text { and } 3 x-y=-1 \\ x+2 y=-1 \text { and } 3 x-y=-1\end{array}\end{array} \)

To find which system of equations has a solution of approximately \( (0.6, -0.8) \), you can substitute \( x = 0.6 \) and \( y = -0.8 \) into each equation of the provided systems. For example, let's check the first system: 1. \( x + 2y = -1 \) - Plugging in values: \( 0.6 + 2(-0.8) = 0.6 - 1.6 = -1 \) (True) 2. \( 3x + y = 1 \) - Plugging in values: \( 3(0.6) + (-0.8) = 1.8 - 0.8 = 1 \) (True) Both equations are satisfied by \( (0.6, -0.8) \), so this system is a candidate! Moving on to some problem-solving tips: Always check the proposed solutions by substituting them back into the equations. It's like a secret handshake to prove you're in the right club! Also, a common mistake is to forget a negative sign when substituting; so stay vigilant, math ninjas! For further exploration, consider textbooks on systems of equations, where you can find numerous examples and practice problems. Additionally, online platforms like Khan Academy and Coursera offer fantastic courses to sharpen your skills further and make math even more enjoyable!