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 for a system of equations to have one solution?

Back

It means that the lines represented by the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the lines represented by the equations coincide, or are the same line.

Front

What is the substitution method for solving linear systems?

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 for solving linear systems?

Back

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

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find two or more points that satisfy the equation and plot them on a coordinate plane, then draw a line through the 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.

Front

How can you find the intersection point of two lines graphically?

Back

The intersection point can be found by locating the point where the two lines cross on the graph.