Kindly check out the below video to learn about 'Substitution and Elimination Method'. Watch the video till the end to solve the tasks.
When graphical methods are imprecise (especially for fractional results), we use Algebraic Methods for exact solutions.
Substitution Method:
Best used when one variable is already isolated or has a coefficient of \(1\).
- Step 1: Express one variable in terms of the other from one equation (e.g., \(x = 3 - 2y\)).
- Step 2: Plug this expression into the other equation.
- Step 3: Solve for the remaining variable.
- Step 4: Substitute that value back into the Step 1 equation to find the first variable.
Elimination Method:
Best used when equations are in standard form (\(ax + by = c\)).
- Step 1: Multiply one or both equations by constants so that the coefficients of one variable are identical (or opposites).
- Step 2: Add or subtract the equations to "eliminate" that variable.
- Step 3: Solve the resulting one-variable equation.
- Step 4: Substitute the value into any original equation to find the other variable.
Important!
If the variables disappear during your calculations, look at the resulting statement:
- False Statement (e.g., \(0 = 5\)): The lines are parallel. No Solution.
- True Statement (e.g., \(0 = 0\)): The lines are coincident (the same line). Infinitely Many Solutions.