Substitution Method

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 inverse operations to get the variable on one side of the equation by itself.

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

Given the equations y = 2x - 11 and 2x - 8y = 4, how do you start solving them using substitution?

Back

You start by substituting the expression for y from the first equation into the second equation.

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the solution to the system of equations y = 7x + 7 and 2y + 2x = -18?

Back

The solution is (-2, -7).

Front

How can you check if your solution to a system of equations is correct?

Back

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

Front

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

Back

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

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

How do you handle a system of equations with no solution?

Back

A system of equations with no solution is called inconsistent, and it occurs when the lines represented by the equations are parallel.