Solving Linear Systems: Graphing, Substitution, Elimination

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

What does it mean to solve a linear system?

Back

To solve a linear system means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What does it mean if a linear system has no solution?

Back

A linear system has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

A linear system has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

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How do you graph a linear equation?

Back

To graph a linear equation, you can find two or more points that satisfy the equation and then draw a straight line through those points.

Front

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

Back

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

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How do you find the intersection of two lines graphically?

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The intersection of two lines is found at the point where the lines cross each other on the graph.

Front

What is the first step in solving a system of equations by substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.