Linear Systems Substitution Method

Front

What is the substitution method in solving linear systems?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into both equations. If both equations are satisfied, the point is a solution.

Front

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

Back

If a system has no solution, it means the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The graphical representation is two identical lines, meaning every point on the line is a solution.

Front

What is the first step in using the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

When is the substitution method preferred over the elimination method?

Back

The substitution method is preferred when one equation is easily solvable for one variable, making substitution straightforward.

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19 using the substitution method?

Back

The solution is (2, 5).

Front

What does it indicate if two lines intersect at a single point?

Back

If two lines intersect at a single point, it indicates that the system of equations has a unique solution.

Front

How can you check your solution after solving a system of equations?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.

Front

What is the significance of parallel lines in the context of linear systems?

Back

Parallel lines indicate that the system of equations has no solution, as they do not intersect.