How to solve simultaneous equations quickly for Singapore E-math exams
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When one equation is already solved for a variable, isolate that term and replace it in the second equation. This reduces the system to a single linear equation that can be solved easily for the first unknown. Once the value is found, substitute it back into either original equation to determine the second variable. Always check your final pair of values against both original equations to ensure accuracy.
Elimination Technique for Coefficients
Multiply one or both equations by constants so that the coefficients of one variable become equal or opposite. Add or subtract the equations directly to eliminate that specific variable and solve for the remaining one. This method is often faster when coefficients are multiples of each other without needing rearrangement. Ensure you simplify the resulting single-variable equation before finding the final solution pair.
Solving Quadratic Simultaneous Systems
Use the substitution method by expressing one variable from the linear equation and substituting it into the quadratic equation. This process creates a quadratic equation in one variable that can be solved using factorisation or the formula. Find both possible values for the first variable and calculate the corresponding second values to form complete solution pairs. Verify all pairs satisfy the original linear and quadratic equations to avoid extraneous solutions.