Systems Review

Front

What is a solution in the context of a system of equations?

Back

A solution is a set of values for the variables that makes all equations in the system true.

Front

What does the inequality y > x + 1 represent graphically?

Back

It represents the region above the line y = x + 1, not including the line itself.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If all equations are satisfied, it is a solution.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What are the steps to solve a system of equations using elimination?

Back

1. Align the equations. 2. Multiply if necessary to match coefficients. 3. Add or subtract equations to eliminate a variable. 4. Solve for the remaining variable.

Front

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

Back

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

Front

What is a system of equations?

Back

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

Front

How can you represent a system of equations graphically?

Back

By plotting each equation on the same coordinate plane and finding the intersection points.

Front

What is the significance of the intersection point of two lines in a system of equations?

Back

The intersection point represents the solution to the system, where both equations are satisfied.

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 is non-negative.