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.

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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 graphical representation of a system of linear equations?

Back

The intersection point(s) of the lines represented by the equations.

Front

What is the solution to a system of linear equations?

Back

The point(s) where the graphs of the equations intersect.

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 does it mean if a system of equations has no solution?

Back

The lines are parallel and do not intersect.

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What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, so every point on the line is a solution.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are satisfied, it is a solution.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.