The image contains a list of linear equations and a set of potential solutions labeled $A, B, C, D, E,$ and $F$. Let’s verify which solution satisfies each equation step by step. The equations are:

1. $2x - y = 9$
2. $x - 5y = 2$
3. $x - y = 16$
4. $2x - y = 5$
5. $x - 3y = 4$

And the points are:

• $A(-2, -2)$
• $B(-2, 4)$
• $C(1, -8)$
• $D(3, 0)$
• $E(12, 2)$
• $F(20, 4)$

Let’s test each equation systematically. Define the equations and points equations = [ lambda x, y: 2 * x - y - 9, # 1. 2x - y = 9 lambda x, y: x - 5 * y - 2, # 2. x - 5y = 2 lambda x, y: x - y - 16, # 3. x - y = 16 lambda x, y: 2 * x - y - 5, # 4. 2x - y = 5 lambda x, y: x - 3 * y - 4 # 5. x - 3y = 4 ]

Points

points = { "A": (-2, -2), "B": (-2, 4), "C": (1, -8), "D": (3, 0), "E": (12, 2), "F": (20, 4) }

Test each equation with each point

results = {} for eq_num, eq in enumerate(equations, start=1): results[eq_num] = [] for label, (x, y) in points.items(): if eq(x, y) == 0: # Check if the point satisfies the equation results[eq_num].append(label)

resultsHere are the results of testing each point against the equations:

1. $2x - y = 9$: No point satisfies this equation.
2. $x - 5y = 2$: Point E (12, 2) satisfies this equation.
3. $x - y = 16$: Point F (20, 4) satisfies this equation.
4. $2x - y = 5$: No point satisfies this equation.
5. $x - 3y = 4$: Point A (-2, -2) satisfies this equation.

Would you like me to explain how these results were obtained in detail?

Here are 5 follow-up questions to consider:

1. Would you like to verify the calculations for specific equations?
2. Should I analyze why certain points do not satisfy specific equations?
3. Would you like me to plot these points and equations graphically?
4. Do you need further analysis for systems of equations involving combinations of these?
5. Should we work on a different method to analyze the results, like substitution or elimination?

Tip: Always substitute the point coordinates directly into the equation to confirm they satisfy it.