Solving Systems of Equations Using Substitution

This video tutorial covers solving systems of equations using algebraic methods, focusing on substitution. It explains how to substitute known values into equations to reduce variables and solve for unknowns. The tutorial includes example problems and practice exercises, highlighting scenarios with infinite solutions and how to identify them.

What is the main goal when using the substitution method to solve a system of equations?

• To eliminate all variables

• To find the slope of the lines

• To convert the system into a one-variable equation

• To graph the equations

In the substitution method, what do you do if you know the value of one variable?

• Divide it by the other variable

• Ignore the value

• Multiply it by the other variable

• Substitute it into the other equation

What is the first step in solving the equation 4x + 6 = 18?

• Divide both sides by 4

• Subtract 6 from both sides

• Add 6 to both sides

• Multiply both sides by 4

After solving for x, what should you do next to solve the system of equations?

• Multiply x by y

• Substitute x back into one of the original equations

• Divide x by y

• Graph the equations

In the second example, what do you substitute for y in the equation 2x - 3y = -1?

• 2x - 1

• 2x + 1

• x - 1

• x + 1

What is the result of combining like terms in the equation 2x - 3(x - 1) = -1?

• x - 3 = 1

• x + 3 = 1

• x - 3 = -1

• x + 3 = -1

What does it mean if you end up with a statement like 10 = 10 when solving a system of equations?

• There is no solution

• There is exactly one solution

• There are infinitely many solutions

• The system is inconsistent

What should you do if you get a fraction as a solution?

• Ignore it

• Accept it as a valid solution

• Check your work for mistakes

• Assume it's incorrect

What does it indicate if the lines in a system of equations are parallel?

• There is one solution

• There is no solution

• There are infinitely many solutions

• The system is dependent

What is the significance of the intersection point in a system of equations?

• It indicates the y-intercept

• It shows the midpoint of the lines

• It is the solution to the system

• It represents the slope of the lines