Substitution Method in Linear Equations

This video tutorial covers the substitution method for solving systems of linear equations. It begins with an introduction to the method, followed by a detailed example of solving for x and y. The video outlines the steps for substitution, including ensuring equations are in slope-intercept form, substituting expressions, solving for variables, and checking solutions by graphing. A new system of equations is introduced, highlighting challenges with fractions. The lesson concludes with a summary and a preview of the next topic, using graphs to estimate solutions.

What is the primary goal of the substitution method in solving linear equations?

• To eliminate all variables

• To substitute one equation into another

• To graph the equations

• To find the slope of the line

In the example provided, what expression is substituted for y in the second equation?

• 3x + 2

• 2x + 4

• 5x - 5

• x - 1

After substituting and simplifying, what is the value of x in the example?

• 2

• 3

• 4

• 5

What is the next step after finding the value of x in the substitution method?

• Solve for another variable

• Substitute x back into one of the original equations to find y

• Check the solution by graphing

• Rewrite the equation in standard form

What is the final value of y in the example provided?

• 9

• 8

• 11

• 10

What is the first step in the substitution method according to the lesson?

• Check the solution

• Solve for x

• Substitute the right side of one equation for y in the other equation

• Graph the equations

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

• By checking if the lines are parallel

• By finding the point of intersection

• By ensuring the lines are perpendicular

• By calculating the slope

What is the slope of the first equation in the graphical representation?

• 1

• -2

• -1

• 0

What is the y-intercept of the second equation in the graphical representation?

• 6

• 5

• 4

• 3

What is an alternative approach to solving the system of equations mentioned in the lesson?

• Graphing the equations

• Isolating x and y

• Using matrices

• Using elimination method