Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if a system of equations has one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, so they intersect at every point on that line.

Front

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

Back

By plotting the equations on a graph and identifying the point(s) of intersection.

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 is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

If two lines are parallel, what can be said about their slopes?

Back

They have the same slope.

Front

What is the slope of the line represented by the equation 3x + 4y = 12?

Back

The slope is -3/4 after rearranging to slope-intercept form.