Algebraic Methods of Solving a Pair of Linear Equations

If the equations represent parallel lines, there is no solution. If they represent the same line, there are infinitely many solutions. This can be determined by comparing the ratios of the coefficients.

Substitute the obtained values of x and y back into the original equations to ensure both equations are satisfied.

Yes, the elimination method is more efficient when the coefficients of one variable are already aligned or can be easily manipulated to align, allowing for quick elimination.

The substitution method is preferable when one equation is easily solvable for one variable, making substitution straightforward.

The steps are: Multiply one or both equations to align coefficients of one variable. Add or subtract the equations to eliminate that variable. Solve the resulting single-variable equation. Substitute the found value into one of the original equations to find the other variable.

The elimination method focuses on eliminating one variable by adding or subtracting equations, whereas the substitution method involves expressing one variable in terms of the other and substituting it into the second equation.

In the substitution method: Solve one of the equations for one variable in terms of the other. Substitute this expression into the second equation. Solve the resulting single-variable equation. Use the obtained value to find the other variable

The primary algebraic methods for solving a pair of linear equations are: Substitution Method: Solve one equation for one variable and substitute this expression into the other equation. Elimination Method: Add or subtract equations to eliminate one variable, simplifying the system to a single-variable equation.