Exploring Solutions to Systems of Equations by Graphing

The video tutorial explains how to solve systems of equations by graphing. It begins with converting equations into slope-intercept form, followed by graphing them on a coordinate plane. The intersection point of the lines is identified as the solution, which is then verified by substituting back into the original equations.

What is the first step in solving systems of equations by graphing?

• Graph each equation on the same coordinate plane

• Check the solution by substituting the values

• Find the intersection point of the lines

• Write the equations in slope-intercept form

What form should the equations be in before graphing?

• Standard form

• Point-slope form

• Slope-intercept form

• Quadratic form

In the equation y = mx + b, what does 'b' represent?

• The y-intercept

• The x-intercept

• The coefficient of x

• The slope

When graphing the equation y = -x + 3, where do you start?

• At the origin

• At the y-intercept, which is 3

• At the slope, which is -1

• At the x-intercept, which is -3

What is the slope of the equation y = -x + 3?

• -3

• 3

• -1

• 1

How do you find the intersection point of two lines on a graph?

• By finding the y-intercepts

• By finding where the lines cross

• By finding the slopes

• By finding the x-intercepts

What is the intersection point of the lines y = -x + 3 and y = -8x - 4?

• (4, -1)

• (-1, 4)

• (1, -4)

• (-4, 1)

How can you verify the solution to a system of equations?

• By graphing the equations again

• By substituting the solution back into the original equations

• By finding the slopes again

• By finding the y-intercepts again

What should the left side of the equation equal when you substitute the solution back into the original equation?

• The right side of the equation

• The y-intercept

• The slope

• The x-intercept

What is the solution to the system of equations x + y = 3 and 8x + y = -4?

• (1, -4)

• (-1, 4)

• (4, -1)

• (-4, 1)