Algebraic and Graphical Solution of Simultaneous Equations in 2 Unknowns

Algebraic Solution of Simultaneous Equations

Simultaneous equations are a set of equations which are all linked together by shared variables.
The algebraic solution involves using either the method of substitution, method of elimination, or the method of equations.
Substitution involves solving one of the equations for one variable in terms of the other and replacing (substituting) it in the other equation.
Elimination involves adding or subtracting the equations in order to eliminate one of the variables.
Equations method involves equating coefficients of the variables after rearrangement and solving the resultant equations.

This involves sketching the graphs of the equations on the same axes.
Each intersection point of the lines represents a solution of the simultaneous equations.
Accuracy of these solutions depends on the quality and scale of the drawing.

Simultaneous equations: These are equations involving more than one variable.
Substitution: This method involves replacing a variable with an expression.
Elimination: This involves making the coefficient of one of the variables the same in both equations so the equations can be added or subtracted.
Intersection point: The point where the graphs of the equations cross, representing the common solution to the equations.