Flashcard Set Up Substitution Problems

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation to find the values of the variables.

Front

What is the first step in substitution when given the equations y = -6x + 5 and -2x + y = 5?

Back

-2x + (-6x + 5) = 5

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the lines represented by the equations: if they intersect at one point, there is one solution; if they are parallel, there are no solutions; if they are the same line, there are infinitely many solutions.

Front

What does it mean if a system of equations has 0 solutions?

Back

It means the lines represented by the equations are parallel and do not intersect.

Front

What is the solution to the system of equations represented by the lines graphed by Steffen?

Back

(-3,-8)

Front

What is the first step in substitution for the equation 12(-3x - 6) + 4y = 3?

Back

12(-3x - 6) + 4y = 3

Front

What is the correct first step for substitution in the equation 11x - (11x) = 3?

Back

11x - (11x) = 3

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

How do you graphically represent a system of equations?

Back

By plotting the lines of each equation on the same coordinate plane and finding their intersection.

Front

What is the significance of the point (-3,-8) in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.