Solving Systems of Equations

The video tutorial explains how to solve a system of equations using three methods: graphing, substitution, and matrices on a TI-84 calculator. It demonstrates each method step-by-step, showing that all methods lead to the same solution, x = 1 and y = 2. The tutorial highlights the advantages of using Desmos for graphing and provides a detailed algebraic process for substitution. It also covers using the TI-84 calculator to solve the system with matrices, confirming the solution's consistency across different approaches.

Which methods were introduced for solving systems of equations?

• Substitution, graphing, and elimination

• Graphing, substitution, and using a matrix on the TI-84

• Elimination, graphing, and using a matrix on the TI-84

• Substitution, elimination, and using a matrix on the TI-84

What is one advantage of using Desmos for graphing equations?

• It requires equations to be in slope-intercept form

• It can only graph equations in standard form

• It can graph equations in both slope-intercept and standard form

• It does not require any form of the equation

What form must equations be in to use the TI-84 for graphing?

• Slope-intercept form

• Any form

• Point-slope form

• Standard form

What is the solution to the system of equations obtained by graphing?

• x = 2, y = 1

• x = 1, y = 3

• x = 1, y = 2

• x = 2, y = 3

In the substitution method, what is substituted into the second equation?

• y = 3x + 5

• x = 3y + 5

• y = -3x + 5

• x = -3y + 5

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

• x = 2

• x = 1

• x = 3

• x = 0

How is the value of y found after determining x in the substitution method?

• By using the matrix method

• By solving for y directly

• By using the graph

• By substituting x into the original equation

What is the y-value obtained using the substitution method?

• y = 1

• y = 3

• y = 2

• y = 0

Which function on the TI-84 is used to solve the system using matrices?

• rref

• solve

• matrix

• rref2

What is the solution to the system of equations obtained using the TI-84 matrix method?

• x = 2, y = 3

• x = 1, y = 2

• x = 1, y = 3

• x = 2, y = 1