Solving Systems of Equations with Substitution

The video tutorial covers systems of equations, focusing on graphing and substitution methods. It explains the three types of solutions: one solution, no solution, and infinite solutions. The tutorial provides examples and practice problems to illustrate these concepts, emphasizing the importance of understanding special cases in systems of equations.

What is the solution when two lines intersect at one point?

• Infinite solutions

• Two solutions

• No solution

• One solution

What does it mean when two lines are parallel?

• They intersect at two points

• They intersect at one point

• They never intersect

• They have infinite solutions

If two lines have the same slope but different y-intercepts, what is the solution?

• One solution

• Infinite solutions

• Two solutions

• No solution

In the substitution method, what is the first step?

• Graph the equations

• Multiply the equations

• Add the equations together

• Solve for one variable in one of the equations

When solving a system with substitution, what should you do after finding the value of one variable?

• Substitute it back into one of the original equations

• Graph the equations

• Multiply the equations

• Stop, you are done

What is the solution to the system if the result is a true statement like 1=1?

• Two solutions

• Infinite solutions

• One solution

• No solution

What does it mean if the variables cancel out and the resulting statement is false?

• No solution

• One solution

• Two solutions

• Infinite solutions

What should you be careful about when substituting a negative value?

• Graphing the equations

• Adding the equations

• Multiplying by zero

• Ignoring the negative sign

What is the result if the variables cancel out and the numbers do not equal each other?

• Two solutions

• One solution

• Infinite solutions

• No solution

What is the graphical representation of a system with infinite solutions?

• Two intersecting lines

• Two lines intersecting at two points

• Two parallel lines

• One line