Solving System of Linear Equation

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 for a system of linear equations to have a solution?

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical representation of a solution to a system of linear equations?

Back

The point where the graphs of the equations intersect.

Front

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

Back

The system has infinite solutions because every point on the line is a solution.

Front

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

Back

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

Front

What is the substitution method in solving systems of linear 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 linear equations?

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

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.

Front

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

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The slope indicates the steepness of the line and the direction it goes (positive or negative).