Solving Systems of Equations

The video tutorial explains how to solve a system of equations using the substitution method. It begins with an overview of the method, followed by a detailed explanation of the steps involved. An example problem is set up and solved, demonstrating the substitution process. The tutorial concludes with verification of the solution through graphing, ensuring the solution is correct.

What is the first step in solving a system of equations using the substitution method?

• Solve for a variable in one of the equations.

• Graph the equations.

• Multiply both equations by a common factor.

• Check the solution.

Why is substitution the most obvious method for the given example?

• Both equations are solved for y.

• The equations have no fractions.

• Both equations are solved for x.

• The equations are linear.

What is the least common multiple used to clear the fractions in the example?

• 20

• 10

• 2

• 5

After clearing the fractions, what is the next step in solving for x?

• Add 25x to both sides.

• Multiply both sides by 10.

• Divide both sides by 13.

• Subtract 70 from both sides.

What is the value of x found in the example?

• 5

• 10

• 15

• 20

Which equation is used to find the value of y after finding x?

• A new equation.

• The first equation.

• The sum of both equations.

• The second equation.

What is the y-coordinate of the solution?

• 10

• 0

• 5

• -5

How is the solution expressed?

• As a graph.

• As an ordered pair.

• As a single number.

• As a fraction.

What method is used to verify the solution graphically?

• Checking the solution algebraically.

• Re-solving the equations.

• Plotting the equations on a graph.

• Using a calculator.

What is the point of intersection of the two lines on the graph?

• (10, 5)

• (5, 10)

• (10, -5)

• (5, -5)