Substitution Method - Linear Systems

Front

What is the substitution method in solving linear systems?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

One solution occurs when the lines intersect at one point, no solution occurs when the lines are parallel, and infinitely many solutions occur when the lines are the same.

Front

What does it mean for two lines to be parallel in a linear system?

Back

Parallel lines have the same slope but different y-intercepts, meaning they will never intersect.

Front

What is the first step in using the substitution method?

Back

Isolate one variable in one of the equations.

Front

If you have the equations y = 2x + 3 and y = -x + 1, how would you use substitution to find the solution?

Back

Set 2x + 3 equal to -x + 1 and solve for x.

Front

What is the solution to the system of equations: 2x + 3y = 6 and y = 2 - (2/3)x?

Back

(0, 2) is the solution.

Front

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

Back

It means the equations represent parallel lines that do not intersect.

Front

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

Back

Substitute the solution back into both original equations to verify that both equations are satisfied.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s).

Front

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

Back

The point of intersection represents the values of the variables that satisfy both equations simultaneously.