Solving Systems of Linear Equations WORD PROBLEMS

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of linear equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How can word problems be represented as systems of equations?

Back

By identifying variables, writing equations based on the relationships described, and using the information given.

Front

What is a variable in the context of linear equations?

Back

A symbol (often x or y) that represents an unknown value in an equation.

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What does it mean for two equations to be consistent?

Back

It means that the equations have at least one solution (they intersect at one or more points).

Front

What does it mean for two equations to be inconsistent?

Back

It means that the equations have no solution (they are parallel and do not intersect).

Front

What is the meaning of the slope in a linear equation?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

What is the y-intercept in a linear equation?

Back

The y-coordinate of the point where the line crosses the y-axis (when x=0).