IndietroSolving Systems of Linear Equations by Elimination definitions
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1/15IndietroSkip to main contentIndietroSystem of Linear Equations
A set of two or more equations with the same variables, solved together to find values that satisfy all equations. Elimination Method
A technique for solving systems by adding or subtracting equations to remove one variable, simplifying the system. Substitution Method
An approach where an expression for one variable is replaced in another equation, reducing the system to a single variable. Standard Form
An arrangement of equations where variables and constants are aligned, typically as ax + by = c, for easy comparison. Coefficient
A numerical factor multiplying a variable in an equation, crucial for aligning and manipulating equations in elimination. Variable
A symbol representing an unknown value in equations, commonly x or y, whose values are determined by solving the system. Constant
A fixed value in an equation, often appearing as the standalone number in standard form. Opposite Sign
A pair of coefficients with equal magnitude but different signs, enabling cancellation when equations are added. Multiple
A value obtained by multiplying a coefficient, used to align terms for elimination. Factor
A number that divides another coefficient evenly, guiding which equation to multiply for elimination. Trial and Error
A process of testing different multipliers to achieve equal and opposite coefficients for variable elimination. Vertical Alignment
The arrangement of equations so corresponding terms are stacked, facilitating addition or subtraction. Isolated Variable
A variable expressed alone on one side of an equation, making substitution straightforward. True Statement
An equation that holds valid when the solution values are substituted, confirming correctness. Pair
A set of values for variables, such as (x, y), that solves the system simultaneously.
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