Solving Systems of Equations by Substitution

Mr. Sullivan introduces a new unit on systems of equations, focusing on solving them using substitution. The video includes a warm-up exercise to evaluate functions, followed by a detailed explanation of the substitution method. Several example problems are solved step-by-step to demonstrate the method, emphasizing the importance of isolating variables and substituting expressions. The video concludes with a reminder to complete related assignments.

What are the methods discussed for solving systems of equations?

• Matrix, determinants, and algebra

• Addition, subtraction, and division

• Substitution, elimination, and graphically

• Factoring, roots, and powers

If f(x) = 3x - 4, what is f(-5)?

• 1

• -19

• 11

• -15

In the substitution method, what is the first step when one variable is already isolated?

• Substitute the isolated variable into the other equation

• Eliminate the isolated variable

• Solve for the second variable

• Graph the equations

What does it mean to isolate a variable in the context of solving systems of equations?

• Substitute values from another equation

• Graph the equation

• Combine like terms on one side

• Express the variable on one side of the equation by itself

What is the result of substituting x = 4 into y = 2x - 1?

• y = 11

• y = 9

• y = 5

• y = 7

After substituting and simplifying 3x + 2(2x - 1) = 26, what is the next step to solve for x?

• Check the solution by substitution

• Graph the equation

• Substitute back into the original equation

• Combine like terms and solve for x

How do you solve for x when you have 5x + 5 = -10?

• x = -5

• x = 3

• x = 5

• x = -3

What is the correct ordered pair solution for the system where y = 2x + 5 and y = -3x - 10?

• (-1, -3)

• (3, 1)

• (-3, -1)

• (1, 3)

What is the value of y when x = 3 in the equation y = -5x + 13?

• y = -2

• y = 13

• y = 2

• y = -13

What should you do after finding the value of x in a system of equations?

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

• Stop as you have found the solution

• Graph the solution on a coordinate plane

• Isolate y in the same equation