Sys. of Linear Equations 9th

Vocabulary

100

What is the solution to a system of linear equations?

The point where the two lines intersect.

200

How many solutions does a system have if the lines intersect once?

One solution.

300

What does it mean if two lines are parallel in a system?

They never intersect (no solution).

400

What does the graph look like if a system has infinitely many solutions?

Answer: The same line.

500

What is the ordered pair that makes both equations in a system true called?

The solution to the system

Graphing Systems

100

If two lines cross at (3,2), what is the solution to the system?

(3,2)

200

Does the system have one solution, no solution, or infinitely many solutions?

y=x+2

y=x−5

Answer: No solution

same slope

300

Solve the system:

y=3x−5

y=−2x+10

x=3

y=4

400

Does the system have one solution, no solution, or infinitely many solutions?

y=3x−2

3x−y=2

Rewrite second equation.

Answer: Infinitely many solutions
(same line)

500

Does the system have one solution, no solution, or infinitely many solutions?

2x+y=5

4x+2y=11

Same left side but different constants → impossible.

No solution

Substitution

100

Question:
Solve the system using substitution:

y=4

x+y=9

Answer:
(5,4)

200

Solve:
y=x+2
y=5

(3,5)

300

Solve:
y=x+1

y= 2x - 2

Solution:
x+1=2x−2x

x=3

y=4

Answer: (3,4)

400

5x+20=5y

-2x+y=7

solve using subsitution

(−1,5)

500

x=y−4 

−2x+3y=6

Solve using substitution

(−6,−2)

Random

100

Find the slope and y intercept.

2x+9y=18

slope= 2/9

yint=2

200

-x+4y=-16

find slope and yint

slope=1/4

yint=-4

300

The sum of two numbers is 45. One number is 4 times the other. FInd the numbers.

9 and 36

400

One number added 3 times to another number is 24.   5 times the first number added to 3 times the other number is 36. Find the numbers

• First number: 3

• Second number: 7

500

The larger of two numbers is 4 more than the smaller. Twice the larger added to the smaller equals 86. Find the two numbers.

• Smaller number = 26

• Larger number = 30

Word Problem

100

Two numbers add to 10. One is 4. What is the other?

6

200

Two numbers add to 12 and differ by 2. What are they?

7 and 5

300

You buy 2 notebooks and 1 pen for $7.
A friend buys 1 notebook and 1 pen for $5.
How much is a notebook?

2

400

You buy 2 pencils and 3 erasers for $9.
You buy 1 pencil and 3 erasers for $7.
How much is a pencil?

2

500

A store sells sandwiches for $5 and pencils for 1 dollar. One day they sold 30 items for $110. How much of each item was sold?

• 20 sandwiches

• 10 pencils