Solving Simultaneous Equations with Algebraic Techniques

The video tutorial explains how to solve simultaneous equations involving a nonlinear equation and a linear equation. It covers substituting the linear equation into the nonlinear one, expanding and simplifying the resulting quadratic equation, and applying the quadratic formula to find solutions. The tutorial emphasizes the importance of accuracy in each step and explains how to pair the solutions correctly. It concludes with a breakdown of the marks allocation for each step in the process.

What is the first step in solving the given simultaneous equations?

• Apply the quadratic formula

• Substitute the linear equation into the nonlinear equation

• Collect like terms

• Expand the quadratic equation

When expanding the expression (2y - 3)^2, what is the result?

• 4y^2 + 12y + 9

• 4y^2 - 6y + 9

• 4y^2 - 12y + 9

• 4y^2 - 12y - 9

After expanding and simplifying, what is the quadratic equation obtained?

• 11y^2 - 24y + 18 = 0

• 8y^2 - 24y + 18 = 0

• 11y^2 - 24y + 18 = 14

• 11y^2 - 24y + 4 = 0

What are the values of a, b, and c in the quadratic equation 11y^2 - 24y + 4 = 0?

• a = 11, b = -24, c = 4

• a = 11, b = 24, c = 4

• a = 11, b = 24, c = 18

• a = 11, b = -24, c = 18

What is the quadratic formula used to solve the equation?

• x = (b ± √(b^2 - 4ac)) / 2a

• x = (-b ± √(b^2 - 4ac)) / 2a

• x = (b ± √(b^2 + 4ac)) / 2a

• x = (-b ± √(b^2 + 4ac)) / 2a

What are the two possible values of y obtained from the quadratic formula?

• y = 2/11 and y = 2

• y = 2/11 and y = 3

• y = 1/11 and y = 2

• y = 2 and y = 3

If y = 2/11, what is the corresponding value of x?

• x = 1

• x = -29/11

• x = 2

• x = 29/11

If y = 2, what is the corresponding value of x?

• x = 2

• x = 0

• x = -1

• x = 1

How many marks are allocated for correctly substituting the linear equation into the nonlinear equation?

• 1 mark

• 2 marks

• 3 marks

• 4 marks

What is a key consideration when expanding brackets in this problem?

• Expand quickly to save time

• Use a calculator for all expansions

• Ensure all terms are positive

• Be clear and accurate to avoid errors in subsequent steps