Master Solving a system of equations by substitution

The video tutorial explains how to solve systems of equations using the substitution method. It covers the basics of substitution, including when to use it, and provides three detailed examples. The tutorial emphasizes the importance of having a variable with a coefficient of 1 or -1 for easier calculations. Each example is solved step-by-step, demonstrating the substitution process and how to find the solution for both variables.

What is the primary advantage of using substitution over elimination when solving systems of equations?

• It is easier when a variable is isolated.

• It requires fewer steps.

• It works for all types of equations.

• It is always faster.

In the example where X + 4Y = 2, what is the first step to solve for X?

• Add 4Y to both sides.

• Subtract 4Y from both sides.

• Divide both sides by 4.

• Multiply both sides by 4.

When substituting X = -4Y + 2 into the second equation, what is the resulting equation?

• 4Y - 2 = 7

• -8Y + 4 + 5Y = 7

• X + Y = 7

• 2X + 5Y = 7

In the second example, what is the value of X when Y = 4?

• 16

• 4

• 8

• 12

What is the first step in solving the equation 3X + Y = 16 for Y?

• Multiply both sides by 3.

• Divide both sides by 3.

• Subtract 3X from both sides.

• Add 3X to both sides.

When no variable has a coefficient of 1, which coefficient is preferred for substitution?

• 3

• 2

• 0

• -1

In the final example, what is the value of Y when X = -7?

• 4

• -7

• -4

• 7

Why is it easier to solve for a variable with a coefficient of -1?

• It avoids fractions.

• It simplifies the equation.

• It requires fewer calculations.

• It is always the correct choice.

What is the final solution for the system where X = 3Y + 5 and Y = -4?

• X = 7, Y = -4

• X = -7, Y = 4

• X = 7, Y = 4

• X = -7, Y = -4

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

• Graphing is the best method.

• Substitution is faster than elimination.

• Choose the method based on the equation.

• Always use substitution.