Worked example: non-equivalent systems of equations | High School Math | Khan Academy

TL;DR

Scarlett and Hansol's systems of linear equations are not equivalent to their teacher's system because the ratio between x and y is the same, but the constant terms are different.

Transcript

• Scarlett and Hansol's teacher gave them a system of linear equations to solve. They each took a few steps that lead to the systems shown in the table below. So this is the teacher system. This is what Scarlett got after taking some steps. This is what Hansol got. Which of them obtained a system that is equivalent to the teacher's system? And just... Read More

Key Insights

• 🥳 The ratio between x and y terms in a system of linear equations determines the slope.
• 🏙️ Different constant terms in two systems result in different y-intercepts and lines that are parallel.
• 😫 Equivalent systems have the same solution or solution set.

Questions & Answers

Q: How can we determine if two systems of linear equations are equivalent?

Two systems of linear equations are considered equivalent if they have the same solution or solution set. This means that all the variables in both systems have the same values when the equations are solved.

Q: Why does the difference in constant terms affect the equivalence of systems?

The constant term determines the y-intercept of a line in the slope-intercept form of an equation. If the constant terms in two systems are different, the lines they represent will have different y-intercepts and won't intersect, making the systems not equivalent.

Q: What does it mean for lines to be parallel?

Parallel lines are lines that never intersect. In terms of systems of linear equations, if two lines are parallel, their systems are not equivalent because the lines do not share any common points.

Q: Can two systems have different constant terms but still be equivalent?

No, two systems of linear equations with different constant terms are not equivalent. For equivalence, the ratio between the x and y terms should be the same, as well as the constant terms.

Summary & Key Takeaways

• Scarlett and Hansol are given a system of linear equations by their teacher.

• Scarlett's system has a different constant term compared to the teacher's system, indicating that they are not equivalent.

• Hansol's system also has a different constant term, leading to the same conclusion that it is not equivalent.