Solving Systems Using Substitution.

Front

What is the substitution method in solving systems of equations?

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 isolate a variable in an equation?

Back

To isolate a variable, you perform algebraic operations (addition, subtraction, multiplication, division) to get the variable on one side of the equation and all other terms on the opposite side.

Front

What is the first step in solving a system of equations using substitution?

Back

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

Front

When using substitution, what do you do after substituting the expression into the other equation?

Back

After substituting, you solve the resulting equation for the remaining variable.

Front

What does it mean for a system of equations to have a unique solution?

Back

A unique solution means that the two equations intersect at exactly one point, resulting in one set of values for the variables.

Front

What is an example of a system of equations that has no solution?

Back

An example is the system: y = 2x + 1 and y = 2x - 3. These lines are parallel and do not intersect.

Front

What is an example of a system of equations that has infinitely many solutions?

Back

An example is the system: 2x + 4y = 8 and x + 2y = 4. The second equation is a multiple of the first, meaning they represent the same line.

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 both original equations to see if they hold true.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of the equations plotted on a coordinate plane, where their intersection points represent the solutions.