Solving Linear Equations with Substitution

This video tutorial teaches how to solve pairs of linear equations algebraically using substitution. It begins with a review of solving one-variable equations and extends this knowledge to linear systems. The tutorial provides three examples, demonstrating substitution, isolating variables, and combining like terms to find solutions. Each example concludes with a verification step to ensure the solution satisfies both equations. The lesson emphasizes that equations can be solved in any order and highlights the convenience of substituting isolated variables.

What is the main focus of this lesson?

• Solving quadratic equations

• Solving pairs of linear equations using substitution

• Solving inequalities

• Graphing linear equations

What is a solution to a pair of linear equations?

• A graph that intersects at one point

• A pair of values that makes both equations true

• A single value that satisfies one equation

• A set of inequalities

In Example 1, what value is substituted for g?

• 3

• 1

• 8

• 5

What is the solution to the equations in Example 1?

• b = 3, g = 5

• b = 5, g = 8

• b = 5, g = 3

• b = 8, g = 3

In Example 2, what is the first step in solving the equations?

• Graph the equations

• Add the equations together

• Substitute g with b + 4

• Isolate b in both equations

What is the solution to the equations in Example 2?

• b = 2, g = 6

• b = 6, g = 2

• b = 3, g = 5

• b = 4, g = 8

In Example 3, what expression is substituted for g?

• 3b + 5

• b + 4

• b + 1

• 2b + 2

What is the solution to the equations in Example 3?

• b = 1, g = 2

• b = 4, g = 3

• b = 2, g = 1

• b = 3, g = 4

What is the final step in solving the equations in each example?

• Solve for a different variable

• Substitute the solution back into the original equations

• Check algebraically that the solution satisfies both equations

• Graph the solution

What method is used to solve the pairs of linear equations in this lesson?

• Substitution

• Factoring

• Graphing

• Elimination