Graphing and Solving Systems of Equations

This lesson focuses on solving systems of equations by graphing. It introduces key vocabulary, explains how to graph systems to find solutions, and provides multiple exercises for practice. Students learn to verify solutions both visually and mathematically. The lesson concludes with instructions for further practice and homework.

What is the main focus of Lesson 25 in Eureka Math?

• Solving systems by elimination

• Solving quadratic equations

• Solving systems by graphing

• Solving systems by substitution

Which of the following best describes a 'system of equations'?

• A single linear equation

• An equation with no solution

• A quadratic equation

• Two or more linear equations related to the same situation

What is the solution to a system of equations?

• The difference between the y-intercepts

• The product of the slopes

• The sum of the coefficients

• The point where the graphs of the equations intersect

When graphing the equation 2y + x = 12, what are the intercepts?

• (0, 6) and (12, 0)

• (6, 0) and (0, 12)

• (0, 0) and (12, 12)

• (0, 12) and (12, 0)

How do you graph the equation y = 5/6x - 2?

• Using the slope-intercept method

• Using the elimination method

• Using the intercepts method

• Using the quadratic formula

What is the solution to the system of equations where the graphs intersect at (6, 3)?

• (0, 6)

• (12, 0)

• (0, 0)

• (6, 3)

How can you verify that a point is a solution to a system of equations?

• By multiplying the coordinates

• By checking if the point lies on both graphs

• By adding the coordinates

• By finding the midpoint

What should you do if a point works for one equation but not the other in a system?

• Conclude it is not a solution to the system

• Ignore the point

• Consider it a solution to the system

• Verify it with another method

What is the purpose of the problem set in the lesson?

• To provide practice on graphing and verifying solutions

• To review previous lessons

• To introduce new concepts

• To test knowledge of quadratic equations

What should you do if you need help with the problem set?

• Guess the answers

• Skip the questions

• Ask the teacher for help

• Use a calculator