Gr 11 Math Ch 2: Substitution

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What is the first step in solving quadratic equations by substitution?

Determine restrictions (correct)

Make the substitution

Verify restrictions

Solve for k

What is the purpose of making a substitution in quadratic equations?

To solve for k

To simplify the equation (correct)

To make the equation more complex

To identify the restrictions

What should you do with the values obtained for k?

Discard them

Leave them as the final answer

Use them to solve for x (correct)

Use them to verify the restrictions

Why do we determine restrictions for k?

To ensure the expression remains defined Signup and view all the answers

What is the final step in solving quadratic equations by substitution?

Write the final answer Signup and view all the answers

What happens to the identified restrictions after solving for k?

They are verified against the solutions Signup and view all the answers

What happens when the values that would make any denominator equal to zero are identified?

These values are not allowed in the solution. Signup and view all the answers

What is the main purpose of determining restrictions for k?

To prevent undefined expressions. Signup and view all the answers

Which statement is true about the repeated expression in quadratic equations?

It is substituted with a simpler variable. Signup and view all the answers

What is the result of solving the simpler quadratic equation in terms of k?

The values of k are used to solve for x. Signup and view all the answers

What happens to the solutions after verifying the restrictions?

They are written as the final answer. Signup and view all the answers

What is the main benefit of solving quadratic equations by substitution?

It simplifies the process significantly. Signup and view all the answers

What is the primary reason for identifying restrictions in the original variable before making a substitution?

To prevent the introduction of extraneous solutions Signup and view all the answers

What is the relationship between the values of the original variable and $k$ after substitution?

The values of $k$ are equivalent to the values of the original variable Signup and view all the answers

What is the primary advantage of solving the quadratic equation in terms of $k$?

It reduces the complexity of the equation Signup and view all the answers

What is the consequence of failing to verify restrictions after solving for $k$?

The solution may not be accurate Signup and view all the answers

What is the purpose of solving for the original variable after solving for $k$?

To express the solution in terms of the original variable Signup and view all the answers

What is the primary difference between the restrictions identified in steps 1 and 3?

The restrictions in step 1 are for the original variable, while those in step 3 are for $k$ Signup and view all the answers

Gr 11 Math Ch 2: Substitution

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