maths

• What are simultaneous equations?


  Simultaneous equations are a set of equations with multiple unknowns that must be solved together.
• In the example given, what are the two equations in the simultaneous equations?


  \begin{align} x +$y =$$10 \\ 2x - y =$ 5 \end{align}
• How do you find values for x and y in simultaneous equations?


  By solving both equations together to satisfy both at the same time.
• What are the common methods for solving simultaneous equations?


  1. Substitution method
  2. Elimination method
  3. Graphical method
  4. Matrix method
• What is the substitution method for solving simultaneous equations?


  It involves expressing one variable in terms of the other and substituting it into the other equation.
• What is the elimination method for solving simultaneous equations?


  It involves adding or subtracting equations to eliminate one variable.
• What is the graphical method for solving simultaneous equations?


  It involves plotting both equations and finding the intersection point.
• What is the matrix method for solving simultaneous equations?


  It involves using matrices to solve the system of equations.
• Given the equations $2x +$$y =$$7$ and $2x - y =$$1$, which method is most efficient to solve them?


  Elimination method is most efficient due to the same coefficients of x.
• What is the first step in the substitution method?


  Choose one equation and rearrange it to express one variable in terms of the other.
• In the example, what is the value of x when solving the equations $x +$$y =$$10$ and $2x - y =$$5$ using substitution?


  $x =$$5$
• What is the value of y when solving the equations $x +$$y =$$10$ and $2x - y =$$5$ using substitution?


  $y =$$5$
• What is the first step in the elimination method?


  Multiply one or both equations by constants to make the coefficients of one variable equal in magnitude but opposite in sign.
• What is the solution for $x$ in the equations $2x +$$y =$$7$ and $x - y =$$1$ using elimination?


  $x =$$\frac{9}{4}$
• What is the solution for $y$ in the equations $2x +$$y =$$7$ and $x - y =$$1$ using elimination?


  $y =$$\frac{5}{4}$
• What are the steps to interpret and check solutions of simultaneous equations?


  1. Interpret the solution in the context of the problem.
  2. Substitute the solution back into both original equations to verify it satisfies them.
• If you found $x =$$2$ and $y =$$3$ for the equations $2x +$$y =$$7$ and $x - y =$$-1$, how do you check if this solution is correct?


  Substitute $x =$$2$ and $y =$$3$ back into both equations to verify.
• What is the final step after solving simultaneous equations?


  To interpret and check the solutions.
• What does it mean to interpret a solution in the context of a problem?


  It means to understand what the values of the variables represent in the real-world scenario.
• How do you check if a solution satisfies the original equations?


  By substituting the solution values back into both original equations.