How to solve a system using substitution no solution

The video tutorial explains how to solve equations using substitution. It begins by introducing the concept of substitution and the importance of isolating a variable. The instructor discusses how to choose which variable to solve for, depending on the given equations. The tutorial then demonstrates the steps to solve the equation, highlighting the importance of the distributive property and combining like terms. It concludes by explaining why some systems of equations have no solution, using the concept of parallel lines, and summarizes the key points of the substitution method.

What is the first step in solving an equation using substitution?

• Isolate one of the variables

• Multiply both sides by a constant

• Divide both sides by a variable

• Add a constant to both sides

When deciding which variable to solve for, what should you consider?

• The variable that appears in both equations

• The variable that is easiest to isolate

• The variable with the largest coefficient

• The variable that appears first in the equation

In the equation X + 5Y = 4, what is the expression for X after solving for it?

• X = 5Y - 4

• X = 4 - 5Y

• X = -5Y + 4

• X = 4 + 5Y

What is the result when you substitute X = -5Y + 4 into the equation 3X - 5Y = -1?

• A single solution for X and Y

• No solution

• Infinite solutions

• A solution only for X

What does it mean when two lines do not intersect?

• They have infinite solutions

• They have a single solution

• They are parallel

• They are perpendicular

What is indicated by the equation 12 = -1 in the context of solving systems of equations?

• A unique solution exists

• The system has no solution

• The system has infinite solutions

• The solution is only for Y

What is the significance of the result when both variables cancel out in a system of equations?

• It shows the system has infinite solutions

• It means the lines intersect at one point

• It suggests the lines are parallel

• It indicates a unique solution