Graphical systems application problem | Systems of equations | 8th grade | Khan Academy | Summary and Q&A

TL;DR

Abby and Ben earned a total of $50, with Abby earning $10 more than Ben.

Key Insights

• 🇧🇯 The problem involves finding the individual earnings of Abby and Ben, given their total earnings and the information that Abby earned $10 more than Ben.
• 📈 Graphing the equations for Abby and Ben's earnings helps visualize the possible solutions.
• 😥 The point of intersection on the graph represents the values of Abby and Ben's earnings that satisfy both constraints.
• 💁 The equations can be rearranged to slope-intercept form to easily graph them.
• 📈 The graph confirms that Abby earned $30 and Ben earned $20.
• ✅ Verifying the solution involves checking if Abby and Ben's earnings satisfy both constraints.

Transcript

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Questions & Answers

Q: How much did Abby and Ben earn in total?

Abby and Ben earned a total of $50 together.

Q: How much more did Abby earn than Ben?

Abby earned $10 more than Ben.

Q: How can this problem be solved graphically?

The problem can be solved by graphing the equations for Abby and Ben's earnings and finding the point of intersection.

Q: How can we interpret the graph?

The graph shows the possible combinations of Abby and Ben's earnings that satisfy the given constraints.

Summary & Key Takeaways

• Abby and Ben earned a total of $50, with Abby earning $10 more than Ben.

• The problem can be solved using graphing techniques.

• The graph shows the points at which Abby and Ben's earnings intersect, indicating their individual earnings.