Systems of Linear Equations And Inequalities

Question 1

How many equations can be inside of a system of a linear equation?

Answer 1

There are typically two equations inside of brackets, but there can be more.

Question 2

When visualizing solutions in a system with two linear equations and two variables, what are intersect lines?

Answer 2

If lines intersect, the system has one solution that intersect. The system is consistent and independent

Question 3

When visualizing solutions in a system with two linear equations and two variables, what are parallel lines?

Answer 3

If the lines are parallel, then the system has no solution because the lines never intersect. The system is inconsistent and independent.

Question 4

When visualizing solutions in a system with two linear equations and two variables, what are coincident lines?

Answer 4

Conincident lines overlap, with infinite solutions.The solution set is the set of all points on the line. The system is consistent and are dependent

Question 5

When solving system of two linear equations using graphing, what’s the first step?

Answer 5

Change the equation to slope intercept form

y= mx + b

mx = slope and b is the y intercept

Question 6

What direction is a line going if it has a slope of

-1/1

Answer 6

-1 is the slope, or angle of the line. 1 is the amount of units you are moving on the x axis. Since 1 is a positive, you are moving to the right one unit. Everytme you move 1 unit space to the right, you go down one.

Question 7

The answer to a system of two linear equations is, when grapphed, the lines intersect. The point of intersectioj is called an _______

Answer 7

ordered pair

Question 8

When is it a good time to use the substitution method when solving a system of two linear equations?

Answer 8

If the x- and the y intercept aren’t integers (…-3,-2,-1,0,1,2,3….) then it’s best to use the substitution method.

Question 9

When using the substituon method. which equation will be easier to find y?

{3x + y = -9}

{-2x + 3y = 17}

Answer 9

Solving for the first equation is easier, since the coefficient is 1.

Question 10

What is the idea behind using the elimination method of solving a system of linear equations?

Answer 10

The basic idea of the elimination method is to get the coefficients of one of the variables to be additive inverses so the equations can be added. It’s best used if the subsitution method leads to confusing fractions.

Question 11

Solve this system of linear equation using the elimination method. What are the ordered pairs?

Answer 11

(4,-5/2)

Question 12

When should you use the substitution method?

Answer 12

If one of the coefficients of the variables is 1 or one of the variables is already solved for (as in x= or y=)

Question 13

When should you use the elimination method?

Answer 13

if both equations are in standard form (Ax+By= C)

Question 14

When solving systems of equations and end up with an inconsistent system like, 0= a nonzero constant), what will the lines look like, graphically?

Answer 14

The lines will be parallel. It has no solution.

Question 15

Solve using substitution or elimination method. Draw a graph to support your solution.

Question 16

translate this into a system of linear equations:

the sum of one number and three times another is -12. The difference of twice the first numbrer and the second number is 32. What are the numbers?

Answer 16

a + 3x = - 12

2a - x = 32

Answers: 12 and -8

Question 17

How do you find a perimeter of a rectangle/square?

Answer 17

Perimeter = 2w +2l

Question 18

Problem: Solve Mixture

Answer 18

Question 19

How does the solution to a system of three equations with three unknowns look like?

Answer 19

(x, y, z)

They are an ordered triple

Question 20

When solving a system of three linear equations containing three variables, what is the best solution to do so?

a. elimination method.
b. substititon method
c. graphing method

Answer 20

a. elimination method

We eliminate one variable by multiplying equations by nonzero constants to get the coefficnet of the variables to be additive inverses. Then we add equation to remove that variable

Question 21

Answer 21

Question 22

tip: stick to removing on one variable

Answer 22

Question 24

Write as augmented matrix

2x + 3y - z = 1

x - 2z + 1 = 0

• 4x - y + 3z = 5
  tip: remember that variables go on the left, and all constants go on the left of the equal sign. you may need to rewrite some if a constant is on the wrong side of the equal sign. For mising variables, write a 0 in its place.

Answer 24

when rewritten:

2x + 3y -z = 1

x + 0y - 2z = -1

-4x - y +3z = 5

As augmented matrix

x y z constants

2 3 -1 1

1 0 -2 -1

-4 -1 3 5