Systems of Equations Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

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

Front

How can you determine the solution of a system of equations graphically?

Back

By graphing the equations on the same coordinate plane and identifying the point(s) where they intersect.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 4?

Back

The solution is the point (1, 3), where the two lines intersect.

Front

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

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

What is the graphical representation of a system with exactly one solution?

Back

Two lines that intersect at a single point.

Front

How do you find the x-intercept of a linear equation?

Back

Set y = 0 in the equation and solve for x.

Front

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of the line, calculated as the rise over run (change in y over change in x).

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.