Solving Systems by Graphing: Part 1 Challenge

The video tutorial explains how to solve a system of equations by graphing. It begins with an introduction to systems of equations, followed by an example where two linear equations are graphed to find their intersection point, which is the solution. The tutorial provides detailed steps for graphing each equation using their slopes and intercepts, and verifies the solution by substituting the intersection point back into the original equations. The video concludes with a summary of the graphing method as a way to solve systems of equations.

What is a system of equations?

• Two or more linear equations with different variables

• A single linear equation

• A quadratic equation

• Two or more linear equations with the same variables

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What are we looking for when solving a system of equations by graphing?

• The slope of the lines

• The y-intercept of the lines

• The ordered pair where the lines intersect

• The x-intercept of the lines

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In the example, what is the solution to the system of equations?

• (0, 0)

• (-3, -4)

• (2, 4)

• (1, 1)

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What is the slope (m) and y-intercept (b) of the first equation?

• m = 1, b = 2

• m = 1/2, b = 3

• m = 2, b = 0

• m = 3, b = 1/2

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How do you plot points using the slope and y-intercept?

• Start at the x-intercept and move according to the slope

• Start at the origin and move according to the slope

• Start at the y-intercept and move according to the slope

• Start at any point and move randomly

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What is the slope (m) and y-intercept (b) of the second equation?

• m = 1, b = 2

• m = 1/2, b = 3

• m = 3, b = 1/2

• m = 2, b = 0

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How can you convert a non-fraction slope into a fraction?

• By putting it over 1

• By dividing it by 2

• By subtracting 1 from it

• By adding 1 to it

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Where do the two lines intersect in the example?

• (1, 1)

• (2, 4)

• (-3, -4)

• (0, 0)

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How do you verify if an ordered pair is a solution to the system of equations?

• By substituting it into both equations and checking for true statements

• By graphing it on a separate graph

• By checking if it lies on the x-axis

• By checking if it lies on the y-axis

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What is the final step in solving a system of equations by graphing?

• Finding the intersection point

• Finding the x-intercept

• Finding the y-intercept

• Finding the slope

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