Solving Systems of Equations

The video tutorial explains how to solve a system of linear equations with two unknowns using two algebraic methods: elimination and substitution. It provides a detailed walkthrough of each method, demonstrating how to eliminate variables and solve for unknowns. The tutorial also discusses verifying solutions graphically by plotting the equations and identifying the point of intersection. The solution is confirmed to be x = 5 and y = -2, presented as an ordered pair (5, -2).

What are the two main algebraic methods to solve a system of equations?

• Graphing and Factoring

• Completing the Square and Substitution

• Elimination and Substitution

• Graphing and Elimination

In the elimination method, what is the goal when adding the equations together?

• To multiply the equations

• To eliminate one of the variables

• To find the product of the variables

• To divide the equations

What is the result of adding the equations 4x + 3y = 14 and -2x - 3y = -4?

• 2x = 10

• 6x = 18

• 6y = 18

• 2y = 10

After finding x = 5 using elimination, what is the next step to find y?

• Add x to y

• Divide x by y

• Substitute x into one of the original equations

• Multiply x by y

What is the first step in the substitution method?

• Add the equations together

• Solve one equation for one variable

• Multiply the equations

• Graph the equations

When using substitution, what do you do after solving one equation for a variable?

• Substitute the expression into the other equation

• Graph the solution

• Add the equations together

• Multiply both equations

What is the value of y when using the substitution method in this example?

• y = -2

• y = 2

• y = -5

• y = 5

What is the final value of x using the substitution method?

• x = 2

• x = 5

• x = -5

• x = -2

What is a third method mentioned for solving systems of equations?

• Using matrices

• Completing the square

• Graphing the equations

• Factoring the equations

What is the point of intersection for the given system of equations?

• (5, 2)

• (-5, -2)

• (5, -2)

• (-5, 2)