Solving Systems
Special Systems
Parallel and Perpendicular Lines
Word Problems
100
Is the point (-5,2) a solution to the system below?
y=3x+10
y=-x-3
No, the point does not satisfy the equation
y=3x+10
100
Determine whether the system has one solution, no solution, or infinitely many solutions. Explain.
The system has no solution because the lines are parallel and will never intersect.
100
The slope of a line is -8.
What is the slope of the parallel line?
Parallel slope: -8
100
What is always the last step when solving word problems?
Write your solution as a sentence in context.
200
Use the graph to solve the system:
The solution is (3,1).
200
Determine whether the system has one solution, no solution, or infinitely many solutions. Explain.
The system has infinitely many solutions because the lines are the same.
200
The slope of a line is -8.
What is the slope of the perpendicular line?
1/8
200
Suppose you have $20 in your bank account. You start saving $5 each week. Your friend has $5 in his account and is saving $10 each week. Write a system of linear equations to represent this situation. (You do not have to solve)
y=5x+20
y=10x+5
300
Solve the system.
2x+5y=-22
10x+3y=22
(4, -6)
300
Determine whether the system of linear equations has one solution, no solution, or infinitely many solutions. Explain.
y=-2x-4
y=2x-4
The system has one solution because the slopes are different. The lines will intersect.
300
Which lines are parallel? Explain.
Lines b and c are parallel (red and green lines) because they have the same slopes (-2)
300
Suppose your class sells gift wrap for $4 per package and greeting cards for $10 per package. Your class sells 205 packages in all and receives a total of $1084. Write a system of linear equations to represent the situation. (You do not have to solve the system.)
x+y=205
4x+10y=1084
400
Solve the system.
y=x+4
y=-x+8
The solution is (2,6).
400
Solve the system.
15x-5y=-20
-3x+y=4
The system has infinitely many solutions.
400
Are the graphs of the lines parallel, perpendicular, or neither?
y=4x+12
-4x+3y=21
Neither, the slopes are 4 and 4/3.
400
The sum of two numbers is 20. Their difference is 4. Write a system of linear equations that describes this situation. (You do not have to solve it)
x+y=20
x-y=4
500
Solve the system.
4x+5y=3
-3x+2y=38
The solution is (-8,7).
500
Solve the system.
y=-6x-2
12x+2y=-6
The system has no solution.
500
Which lines are perpendicular? Explain.
Line a:
y=6x-2
Line b:
6y=-x
Line c:
y+6x=1
Lines a and b are perpendicular because they have opposite reciprocal slopes (6 and -1/6)
500
You sell bracelets for $2 each and necklaces for $3 each at a local flea market. You collect $95, selling a total of 37 jewelry items. How many of each type of jewelry did you sell?
You sold 16 bracelets and 21 necklaces.