Solving Systems of Linear Equations by Graphing
Solving Systems of Linear Equations by Substitution
Solving Systems of Linear Equations by Elimination
Solving Special Systems of Linear Equations
100
Solve the system of linear equations by graphing:
y = 2x + 9
y = -x + 6
(-1,7)
100
Solve the system of linear equations by substitution:
y = x - 4
y = 4x - 10
(2,-2)
100
Solve the system of linear equations by elimination:
x + 3y = 5
-x - y = -3
(2,1)
100
Solve the system of linear equations:
y = 2x - 2
y = 2x + 9
No solution.
200
Solve the system of linear equations by graphing:
y = x + 4
y = -x + 2
(-1,3)
200
Solve the system of linear equations by substitution:
y = 2x + 5
y = 3x - 1
(6,17)
200
Solve the system of linear equations by elimination:
x - 2y = -7
3x + 2y = 3
(-1,3)
200
Solve the system of linear equations:
y = 3x + 1
-x + 2y = -3
(-1,-2)
300
Solve the system of linear equations by graphing:
y = 2x + 5
y=1/2 x-1
(-4,-3)
300
Solve the system of linear equations by substitution:
x = 2y + 7
3x - 2y = 3
(-2, -4.5)
300
Solve the system of linear equations by elimination:
2x + 7y = 1
2x - 4y = 12
(4,-1)
300
Solve the system of linear equations:
y = 5x - 9
y = 5x + 9
No solution.
400
Solve the system of linear equations by graphing:
x + y = 7
y = x + 3
(2,5)
400
Solve the system of linear equations by substitution:
2x = y - 10
x + 7 = y
(-3,4)
400
Solve the system of linear equations by elimination:
2x - y = 0
3x - 2y = -3
(3,6)
400
Graph:
y ≤-2x+1
y ≤-2x-3
500
Is it possible for a system of linear equations to have exactly two solutions? Explain your reasoning.
No, two lines cannot intersect in exactly two points.
500
Solve the system of linear equations by substitution:
y - x = 0
2x - 5y = 9
(-3,-3)
500
Solve the system of linear equations by elimination:
x + 4y = 1
3x + 5y = 10
(5,-1)
500
Graph the inequality:
y ≥1/3 x+5
y<1/3 x-6
1000
Solve the system of linear equations:
y = 8x - 2
y - 8x = -2
Infinitely many solutions.
1000
The length of a rectangle is equal to triple the width. Write a system of equations to find the dimensions of the rectangle if the perimeter is 96 centimeters? What are the length and the width of the rectangle?
1. define the variables
2. write the system
3. Solve the system
4. Write a sentence for the solution (with units).
1. L = lenght of rectangle (cm)
W = width of rectangle (cm)
2. 86 = 2L + 2W
L = 3W
3. L = 36, W = 12
4. The length is 36 cm and the width is 12 cm.
1000
The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156. How many sundaes and banana splits did the store sell on that sunny day?
1. define the variables
2. write the system
3. Solve the system
4. Write a sentence for the solution (with units).
1. s = # of sundaes sold
b = # of bs sold
2. 156 = 2s +3b
s = b +8
3. b = 28, s = 36
4. The store sold 28 banana splits and and 36 sundaes on that hot summer day.