Substitution Method in Algebra

This video tutorial explains how to solve a system of linear equations using the substitution method. It begins with an introduction to linear equations and their graphical representation, highlighting the challenges of graphing systems of equations. The tutorial then introduces the substitution method as an algebraic solution, providing a step-by-step guide and a detailed example problem. The video concludes with a recap of the substitution method and its application.

What is a linear equation?

• An equation that forms a curve when graphed

• An equation that forms a straight line when graphed

• An equation with no variables

• An equation that forms a circle when graphed

What does the solution to a linear equation represent?

• The point where the line intersects the x-axis

• All the points that do not fall on the line

• The point where the line intersects the y-axis

• All the points that fall on the line

What is a system of linear equations?

• A single linear equation

• Two or more linear equations

• A quadratic equation

• An equation with no solution

What is the solution to a system of linear equations?

• The point where the two lines are perpendicular

• The point where the two lines intersect

• The point where the two lines are parallel

• The point where the two lines are tangent

Why might graphing a system of equations be inconvenient?

• The graph is always easy to interpret

• The intersection point is always an integer

• The equations are always in slope-intercept form

• The equations might not be in a graph-friendly format

What is the slope-intercept form of a linear equation?

• y = b + mx

• x = my + b

• x = b + my

• y = mx + b

What is the goal of the substitution method?

• To find the slope of the line

• To reduce to one equation with one variable

• To eliminate all variables

• To graph the equations

What is the first step in the substitution method?

• Solve for y

• Eliminate all variables

• Find a variable with a coefficient of 1 or -1

• Graph the equations

Why is it useful to find a variable with a coefficient of 1?

• It makes the graph easier to draw

• It simplifies the substitution process

• It eliminates the need for algebra

• It ensures the solution is an integer

What happens if the coefficient is not 1?

• You cannot solve the equation

• You must graph the equation

• The solution is always zero

• You may have to deal with fractions