Exploring Linear Systems and Substitution Methods

What is the solution to a linear system represented by?

• A graph

• A single point

• A set of points

• A single equation

Why is graphing not the most accurate method for finding the solution to a linear system?

• It requires too much time

• It's too accurate

• It's too complex

• It involves estimation

What does the solution to a linear system represent graphically?

• The slope of the lines

• The y-intercept of the lines

• The point where both lines intersect

• The x-intercept of the lines

What is the first step in the substitution method?

• Solve for x in both equations

• Graph both equations

• Substitute y in one equation

• Solve one of the equations for one of its variables

What is the main advantage of the substitution method over graphing?

• It requires less knowledge of algebra

• It provides an exact solution

• It is faster

• It is easier to understand

After solving for one variable in one equation, what is the next step in the substitution method?

• Graph the equation

• Substitute the expression into the other equation

• Check the solution in both equations

• Solve for the other variable in the same equation

What is the result of substituting the solved variable into the other equation?

• A graph

• An equation with only one variable

• An equation with both variables

• An equation with no variables

How do you find the value of the second variable in the substitution method?

• By adding the equations together

• By graphing the equations

• By substituting the known value into one of the original equations

• By solving the second equation for the first variable

Why is it important to check the solution in both equations?

• To find more solutions

• To ensure it's the real solution

• To practice algebra

• To make the solution more accurate

What is the final step after finding the values of both variables in the substitution method?

• Solve the equations again

• Graph the solution

• Check the solution in both equations

• Substitute the variables back into the original equations