Solving Systems of Equations: Graphing and Substitution Techniques

The video tutorial reviews solving systems of linear equations using graphing and substitution methods. It explains when to use each method, provides examples, and highlights the importance of converting equations to slope-intercept form for graphing. The tutorial also covers solving for one variable in substitution and demonstrates both methods with practical examples.

What are the two methods discussed for solving systems of linear equations?

• Graphing and Elimination

• Graphing and Substitution

• Substitution and Elimination

• Graphing and Factoring

When is it a good idea to solve a system of equations by graphing?

• When the equations are in standard form

• When the equations have no solution

• When the equations are difficult to solve algebraically

• When it is easy to convert the equations to slope-intercept form

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

• x = my + b

• y = ax^2 + bx + c

• ax + by = c

• y = mx + b

What should you ensure when graphing by hand?

• The coordinates are integers

• The coordinates are irrational numbers

• The coordinates are fractions

• The coordinates are decimals

What is the first step in graphing a line?

• Graph the midpoint

• Graph the y-intercept

• Graph the x-intercept

• Graph the slope

What is the slope of the line y = 4x - 9?

• -4

• 9

• -9

• 4

When is it a good idea to use the substitution method?

• When the equations have no solution

• When the equations are difficult to graph

• When the equations are in standard form

• When it is easy to solve for one variable in at least one equation

What is the first step in solving a system using substitution?

• Combine the equations

• Solve for one variable in one of the equations

• Graph the equations

• Find the point of intersection

What do you do after solving for one variable in the substitution method?

• Find the point of intersection

• Substitute the value into the other equation

• Combine the equations

• Graph the equations

What is the solution to the system of equations if x = 7 and y = -1?

• (-7, -1)

• (7, 1)

• (7, -1)

• (-7, 1)