Solving Systems by Substitution

Solve the following system of equations by substitution: 2x + y = 7, x - 3y = -5

• x = 1, y = 2

• x = 4, y = 5

• x = 3, y = 4

• x = 2, y = 3

A 3x3 system of equations involves how many variables?

• 4

• 2

• 5

• 3

In a word problem involving solving by substitution, what is the first step you should take?

• Substitute both equations into each other

• Multiply both equations together

• Guess the solution

• Solve one of the equations for one variable in terms of the other variable.

What is the general strategy for solving a 3x3 system of equations by substitution?

• Guessing the values of variables

• Ignoring one of the equations

• The general strategy for solving a 3x3 system of equations by substitution involves solving one equation for a variable, substituting that expression into the other equations, and then solving the resulting equation.

• Solving all equations simultaneously

If you substitute the value of y from one equation into the other equation, what method are you using to solve the system?

• Matrix method

• Graphing method

• Elimination method

• Substitution method

What is the key advantage of using substitution to solve systems of equations?

• Prone to errors and mistakes

• Limited applicability to specific types of equations

• Straightforward and easy to implement

• Complex and time-consuming process

In a 3x3 system of equations, how many equations are involved?

• 2

• 5

• 3

• 4

When solving a word problem using substitution, why is it important to define your variables clearly?

• To save time by not having to define variables.

• To add unnecessary complexity to the problem.

• To confuse the reader and make the problem more challenging.

• To ensure that the values substituted into the equations accurately represent the quantities they stand for.

How can you check your solution after solving a system of equations by substitution?

• Verify that the equations have the same slope

• Check if the solution is an integer

• Verify that both equations are true when the solution values are plugged back in.

• Substitute the solution into one equation only

What is the result of solving the system of equations by substitution: 3x - 2y = 6, 2x + y = 9?

• x = 3, y = 1

• x = 2, y = 5

• x = 4, y = 1

• x = 5, y = -1