Solving Linear Systems by Substitution

This video tutorial explains how to solve linear systems of equations using the substitution method. It begins with an introduction to the concept, followed by detailed steps to isolate variables and solve for x and y. The tutorial includes multiple examples, highlighting strategies to avoid fractions and simplify calculations. By the end, viewers will understand how to apply substitution to find solutions for linear systems.

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

• Add the equations together

• Multiply both equations by a constant

• Isolate one of the variables

• Graph the equations

Why is it beneficial to choose the variable with the lowest coefficient when isolating a variable?

• It simplifies the graphing process

• It makes the calculations faster

• It helps avoid fractions

• It ensures the solution is unique

After isolating a variable in the first equation, what should be done next?

• Check the solution with a calculator

• Substitute it back into the same equation

• Substitute it into the second equation

• Solve for the other variable directly

In the second example, why is the second equation chosen for substitution?

• It has fewer terms

• It results in a simpler graph

• The numbers are multiples of each other

• It has smaller coefficients

What is the advantage of solving for the variable with the lowest coefficient?

• It reduces the number of steps

• It avoids the use of fractions

• It makes the solution more accurate

• It simplifies the graphing process

In the third example, why is the first equation preferred despite the presence of fractions?

• It has more terms

• It results in fewer fractions

• It has a higher coefficient

• It is easier to graph

How can fractions be eliminated when solving equations?

• By subtracting the numerator from both sides

• By multiplying every term by the denominator

• By adding a constant to both sides

• By dividing every term by the numerator

What is the final step after finding the value of one variable?

• Verify the solution with a calculator

• Graph the solution

• Check the solution with another method

• Substitute it back to find the other variable

What is the ordered pair solution for the second example?

• (3, 4)

• (4, 3)

• (2, 1)

• (1, 2)

What should you do if you want more examples or resources?

• Check the links in the description

• Rewatch the video

• Ask a friend for help

• Search online for similar problems