Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Definition: Simultaneous equations are a set of two or more equations with the same variables that are solved together to find a common solution.
Linear Simultaneous Equations: At Grade 8, these consist of two equations representing straight lines. The solution is the point where the lines intersect.
Substitution Method: Solving one equation for one variable (e.g., ) and substituting this expression into the second equation.
Elimination Method: Adding or subtracting the equations to 'eliminate' one variable, making it possible to solve for the remaining one.
Consistency: A solution must satisfy both equations simultaneously. Always check your final values in both original equations.
📐Formulae
General Form:
Slope-Intercept Form:
Elimination Rule: If coefficients of a variable are the same, subtract the equations. If they are opposite (e.g., and ), add the equations.
💡Examples
Problem 1:
Solve using Substitution:
Solution:
Explanation:
Substitute for in the second equation: . Expand: . Simplify: , so . Plug back into the first equation: .
Problem 2:
Solve using Elimination:
Solution:
Explanation:
The coefficients of are opposites ( and ), so add the equations: . This gives , so . Substitute into equation 1: .
Problem 3:
Solve by equating coefficients:
Solution:
Explanation:
Multiply the first equation by to match the coefficients: . Now subtract equation 2 from this new equation: . This results in . Substitute into the first equation: .