Systems of Equations

Vocabulary

100

An ordered pair that makes both linear equations true when substituting it into the specified variables is called the _____________.

Solution to a system of linear equations

200

The three different methods we have learned to solve a system of equations are called:

1.

2.

3.

1. Graphing

2. Substitution

3. Elimination

300

The three different solution types we can have when solving a system of linear equations are:

1.

2.

3.

1. One solution

2. No solution

3. Infinitely many solutions

400

We need to get our linear equations into one of what two forms before we can attempt to solve them using one of our methods?

Slope-intercept form

or

Standard form

Solution Types

100

In a system of linear equations the two linear equations have the same slope and the same y-intercept, what type of solution set is it?

Infinitely many solutions

200

In a system of linear equations the linear equations have the different slopes. What type of solution set is the system?

One solution

300

In a system of linear equations the two linear equations have the same slope but different y-intercepts. What type of solution set is the system?

No solution

400

The system of linear equations is given below, what is the solution set?

y = 2x + 3

2y = 4x + 6

Infinitely many solutions

Solve by Graphing

100

When solving a system of equations by graphing first we must get our linear equations into one of what two forms of linear equations?

Slope-intercept form (y=mx+b)

or

Standard form (Ax + By = C)

200

To graph an equation in slope intercept form first you must plot the ____ - _____________ on the y-axis, then you use the _________ to plot the next point, finally you connect the points with a line and extend it in both directions

y-intercept

slope

300

To graph an equation in standard form first you must substitute a ______ into x, then solve the equation for the "y" variable, that will be the ___-__________. Then repeat the process for the other variable. Finally connect the two points with a line and extend it in both directions. 

"0" zero 

y-intercept

400

The system of linear equations is given below, what is the slope and y-intercept of each of the equations?

y = -2x - 4

y = 2/3 x + 2

m = -2/1    b = (0,-4)

m = 2/3     b = (0,2)

Solve by Substitution

100

To solve a system of linear equations by substitution we must first ______________ a variable in one of the linear equations. Then we substitute what the variable is equal to in place of itself in the other equation. 

isolate 

200

What form of a linear equation is easiest to solve using the substitution method?

slope-intercept form

300

The system of equations is shown below, what is the solution of the system of equations?

y = 2x + 4

y = x - 1

(-5,-6)

400

What is the solution to this system of linear equations?

-2y = -4x + 8

2y + 2x = -2

(1,-2)

Solve by Elimination

100

To solve a system of linear equations using the elimination method first we must line up all corresponding parts ______________. Then, we have to make sure the coefficients of the same variable are __________ coefficients. 

vertically

opposite

200

What form of linear equation is easiest to solve using the elimination method?

standard form

300

What is the solution to the following system of equations?

3x - 2y = 6

x + 2y = 2

(2,0)

400

What is the solution to the following system of linear equations?

2x - y = 8

4x + 2y = 8

(3,-2)