STAAR Systems

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 where the equations intersect on a graph.

Front

What does it mean for an ordered pair to be a solution to a system of equations?

Back

An ordered pair is a solution to a system of equations if it satisfies all equations in the system, meaning it makes all equations true when substituted.

Front

How can you determine if an ordered pair is a solution to a system of equations?

Back

To determine if an ordered pair is a solution, substitute the x and y values into each equation. If both equations are true, the pair is a solution.

Front

What is the x-coordinate of the solution in a system of equations?

Back

The x-coordinate of the solution is the value of x at the point where the two lines representing the equations intersect on a graph.

Front

What is the y-coordinate of the solution in a system of equations?

Back

The y-coordinate of the solution is the value of y at the point where the two lines representing the equations intersect on a graph.

Front

What does it mean if two lines on a graph are parallel?

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system of equations.

Front

What does it mean if two lines on a graph intersect at one point?

Back

If two lines intersect at one point, it means there is exactly one solution to the system of equations, which is the point of intersection.

Front

What does it mean if two lines on a graph coincide?

Back

If two lines coincide, they lie on top of each other, meaning there are infinitely many solutions to the system of equations.

Front

How can you represent a linear relationship on a graph?

Back

A linear relationship can be represented on a graph by plotting points that satisfy the equation and connecting them to form a straight line.

Front

What is the slope of a line?

Back

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