Download CP Geometry Topic I Assignment 6 Name I. Algebra Review

CP Geometry
Topic I Assignment 6
Name _________________________
I. Algebra Review
Becoming a successful Geometrist requires a really good grasp of basic algebraic techniques. The
following problems at the beginning of each assignment will provide you with an opportunity to assess your
algebraic skills relative to the types of algebraic problems / techniques you will encounter this semester in
Geometry.
D. In Algebra we frequently encounter problems with more than one variable. The same is true in
Geometry, so we need to be able to solve systems of equations with more than one variable.
Solve the following systems of linear equations for the indicated variables. Show and justify your steps as
in the following example:
Example 1: Given 2𝑥 − 3𝑦 = 7 and 3𝑥 + 2𝑦 = 30, solve for x and y.
Secret for writing an explanation – label each equation as they appear.
2𝑥 − 3𝑦 = 7
3𝑥 + 2𝑦 = 30
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Eq. 1:
Eq. 2:
Multiply Eq. 1 by the coefficient of x in equation 2:
Distribute the 3
Multiple Eq. 2 by the coefficient of x in equation 1:
Distribute the 2
Subtract Eq. 3 from Eq. 4
Step 6: Divide by 13
Step 7: Replace y with 3 in equation 1:
Step 8: Distribute the 3
Step 9: Add 9 to both sides
Step 10: Divide by 2
3 ∗ (2𝑥 − 3𝑦 = 7)
6𝑥 − 9𝑦 = 21
2 ∗ (3𝑥 + 2𝑦 = 30)
6𝑥 + 4𝑦 = 60
-(6𝑥 − 9𝑦 = 21)
13𝑦 = 39
𝑦=3
2𝑥 − 3(3) = 7
2𝑥 − 9 = 7
2𝑥 = 16
𝑥=8
Check your work: Replace y with 3 and x with 8 in equation 2: 3(8) + 2(3) = 30
30 = 30
(1)
x−y =5
x+y =9
Page 1
𝑥 = __________
Eq. 3
Eq. 4
Eq. 3
check
𝑦 = __________
Fall, 2015-2016
(2)
2m − k = 6
3m − 2k = 7
(3)
p − 3t = 2t + 5
5t = 23 − 2p
𝑝 = __________
𝑡 = __________
(4)
3x + 4y = 6
2y − 3x = 5
𝑥 = __________
𝑦 = __________
(5)
6a − 3b = 7
2b = 8 + 3a
𝑎 = __________
𝑏 = __________
Page 2
𝑘 = __________
𝑚 = __________
Fall, 2015-2016
II. Geometry Problems
In the figures below, ̅̅̅̅
AB and ̅̅̅̅
CD are straight line segments. Find the value of x and/or y in each diagram
below. Show all the steps to your solution and give reasons for your calculations.
1.
x=
y=
Steps and reasons:
2.
x=
Steps and reasons:
3.
x=
Steps and reasons:
y=
𝑥=
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Fall, 2015-2016
4.
x=
Steps and reasons:
y=
5.
x=
Steps and reasons:
y=
6.
x=
Steps and reasons:
y=
Page 4
Fall, 2015-2016
Find the unknown (labeled) angles. Give reasons for your solutions.
7. m∠𝑎 =
Reasons:
8. m∠𝑏 =
m∠𝑐 =
Reasons:
9. m∠𝑑 =
m∠𝑒 =
Reasons:
10. m∠𝑓 =
Reasons:
Page 5
Fall, 2015-2016