Algebra 1 Unit 5

Question 1

What is a system of equations?

Answer 1

Two or more equations with the same variables

Question 2

What is the solution, graphically, to a system?

Answer 2

The point (x,y) where the two lines intersect

Question 3

What is the solution, algebraically, to a system?

Answer 3

The point (x,y) that makes bothe equations true

Question 4

What are the three types of solutions a system can have?

Answer 4

Intersecting lines, parallel lines, and the same line

Question 5

How many solutions do intersecting line have?

Answer 5

It has one solution written as a point (x,y)

Question 6

How many solutions do parallel lines have?

Answer 6

They have no solution written as a circle with a line through it

Question 7

How many solutions do two same lines have?

Answer 7

They have infinitely many written as a sideways 8

Question 8

What are the three steps to solve a system by graphing?

Answer 8

1. Rewrite the equations in slope intercept form
2. Graph the Lines
3. Identify the solution(s)

Question 9

If a system of linear equations has one solution, what does this mean about the two lines?

Answer 9

The lines intersect

Question 10

If a system of linear equations has no solution, what does this mean about the two lines?

Answer 10

The lines are parallel

Question 11

If a system of linear equations has infinately many solutions, what does this mean about the two lines?

Answer 11

The lines are the same

Question 12

What is the substitution method of solving systems?

Answer 12

It substitutes one equation within the other

Question 13

What is the first step when solving a system by substitution?

Answer 13

Solve one equation for x or y

Question 14

When should you use substitution?

Answer 14

When you can isolate a variable with no coefficient

Question 15

What is the elimination method of solving equations?

Answer 15

It adds or subtracts two equations to eliminate a variable

Question 16

What is the first step when solving a system by elimination?

Answer 16

Line the equations up for all parts

Question 17

What if eliminatin systems have no common coeficients?

Answer 17

Multipy one or both equations by some number to create matching/opposite coefficients

Question 18

What is a linear inequality?

Answer 18

Similar to a linear equation, but uses an inequality symbol

Question 19

What is a possible solution to a linear inequality?

Answer 19

Any of the oredered pairs that make the inequality true

Question 20

Is (2,5) a solution of 2x - 3y < 15?

Answer 20

Yes! -11< 15

Question 21

Is (-1, -7) a solution of 2x - 3y < 15?

Answer 21

No! 19 < 15

Question 22

Is (3, -4) a solution of 2x - 3y < 15?

Answer 22

No! 18 < 15

Question 23

Is (0,0) a solution of 2x - 3y < 15?

Answer 23

Yes! 0 < 15

Question 24

What is the best test point when shading a graphed inequality?

Answer 24

The origin (0,0)

Question 25

A greater symbol means shade __________.

Answer 25

Above, make sure y is on the left side of the inequality though

Question 26

A less symbol means shade __________.

Answer 26

Below, make sure y is on the left side of the inequality though

Question 27

Graph a solid line when the inequality sign is ________.

Answer 27

Equal to

Question 28

Graph a dotted line when the inequality sign is ________.

Answer 28

Only greater or less than

Question 29

What would create a sign to flip/change directions?

Answer 29

When you multiply or divide by a negatove value

Question 30

What is a systems of linear inequalities?

Answer 30

Two or more linear inequalities that are graphed together

Question 31

What is the solution to a system of linear inequalities?

Answer 31

The solution is the overlapping region of points that satisfies both inequalities