Solving Systems of Equations by Graphing

The video tutorial explains how to solve a system of equations using the graphing method. It begins by introducing the concept of systems of equations and the need for two equations to solve for two variables. The tutorial then demonstrates how to graph two lines, Y = 3x + 1 and Y = X + 6, by identifying their slopes and y-intercepts. The intersection point of these lines, which is the solution to the system, is found to be (2, 4). Finally, the solution is verified by substituting the values back into the original equations.

What do we need to solve for two separate variables?

• Three separate equations

• One equation

• Two separate equations

• Four separate equations

What method are we using to solve the system of equations in this section?

• Substitution method

• Elimination method

• Graphing method

• Matrix method

What is the y-intercept of the line y = 3/2x + 1?

• 0

• 1

• 3

• 2

What is the slope of the line y = 3/2x + 1?

• 1/2

• 3/2

• 2/3

• 1

What is the y-intercept of the line y = -x + 6?

• 6

• 0

• 3

• 1

What is the slope of the line y = -x + 6?

• -1

• 1

• 0

• 6

At what point do the two lines intersect?

• (1, 2)

• (2, 4)

• (3, 6)

• (4, 8)

What does the point of intersection represent in a system of equations?

• The x-value only

• The y-value only

• The solution to the system

• The midpoint of the lines

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

• By graphing another line

• By substituting the values back into the original equations

• By using a calculator

• By finding another point of intersection

What is the result when you substitute x = 2 and y = 4 into the first equation y = 3/2x + 1?

• 4 = 4

• 4 = 5

• 4 = 6

• 4 = 3