Solving Systems Algebraically

Flashcards on Solving Systems Algebraically using Substitution and Elimination Methods.

What are the two main algebraic methods for solving a system of equations?

Substitution and Elimination

In the substitution method, after isolating a variable from one equation, where should you substitute this expression?

Into the other equation.

When using the elimination method, what condition must be met by the variable you intend to eliminate?

The variable must have the same coefficient in both equations.

After solving for one variable in a system of equations, what is the next step?

Substitute the known value into one of the equations to solve for the other variable.

How should solutions to a system of equations be stated?

As an ordered pair (x, y).

In a linear-quadratic system, which variable is typically isolated?

y

What does solving a system of equations graphically represent?

Finding the points of intersection.

What are the two equations needed to solve Class Example 1?

2x + y = 5 and x + y = 3

According to class example 1, what is the first step in solving for the system of equations?

Isolate the easiest variable first.

What are the two equations needed to solve Class Example 2?

5x - y = 10 and x^2 + x - 2y = 0

According to Class Example 2, what is the first step in solving for the system of equations?

Label each equation.

What two equations are needed to solve class example 3?

x + 2y = 46 and x^2 - 3y = 93

Class Example 3 uses what method to solve the problem?

The Elimination Method

What are the two height equations in class example 4?

h = −4.9t² +700 and h=-5t+650

What is the name of the formula used to solve class example 4?

Quadratic Formula

In Class Example 5, what should you do with the like terms?

Always arrange like terms above each other

What are the two equations needed to solve Class Example 5?

3x^2-x-y-2=0 and 6x^2+4x-y=4

In the kinetic and potential energy example, at what condition does the ball have the same amount of kinetic energy as potential energy?

Ek = Ep

What are the two energy equations needed to solve Class Example 6?

Ek = 5/32 (d-20)^2 and Ep = 5/32 (d-20)^2 + 62.5

When rearranging equations for elimination, what must you be left with?

Only one variable.