Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

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

What is the graphical method for solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

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The system has infinitely many solutions because the lines are the same.

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into the original equations to see if they hold true.

Front

What is the first step in solving the system: y = 2/3x - 2 and y = -x + 3?

Back

Set the two equations equal to each other: 2/3x - 2 = -x + 3.

Front

What is the solution to the system: y = 2x + 1 and y = 4x - 1?

Back

(1, 3) is the solution.