Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 20: The Rectangular Coordinate System
Answer/Discussion
to 1a
A(3, 1), B(2, 1/2), C(2, 2), and D(0,1)
A(3, 1) lies in quadrant I.
B(2, 1/2) lies in quadrant III.
C(2, 2) lies in quadrant IV.
D(0, 1) lies on the y axis.
(return to problem
1a) 
Answer/Discussion
to 2a
Since point A corresponds to 4 on the xaxis
and 2 on the yaxis, then A's ordered pair
is (4, 2).
Since point B corresponds to 0 on the xaxis
and 4 on the yaxis, then B's ordered pair
is (0, 4).
Since point C corresponds to 2 on the xaxis
and 2 on the yaxis, then C's ordered pair
is (2, 2).
Since point D corresponds to  4 on the xaxis
and 0 on the yaxis, then D's ordered pair
is ( 4, 0).
Since point E corresponds to 2 on the xaxis
and 3 on the yaxis, then E's ordered pair
is (2, 3).
Since point F corresponds to 3 on the xaxis
and 3 on the yaxis, then F's ordered pair
is (3, 3).
(return to problem
2a) 
Answer/Discussion
to 3a
y = 4x  10 (0, 10), (1, 14), (1, 14) 
Let's start with the ordered pair (0, 10).
Which number is the x value and which one
is the y value? If you said x = 0 and y = 10, you are correct!
Let's plug (0, 10) into the equation and see what we get: 

*Plug in 0 for x and 10 for y 
This is a TRUE statement, so (0, 10) is a solution to the equation y = 4x  10.
Now, let's take a look at (1, 14).
Which number is the x value and which one
is the y value? If you said x = 1 and y = 14, you are right!
Let's plug (1, 14) into the equation and see what we get: 

*Plug in 1 for x and 14 for y

This is a FALSE statement, so (1, 14) is NOT a solution to the
equation y = 4x  10.
Now, let's take a look at (1, 14).
Which number is the x value and which one
is the y value? If you said x = 1 and y = 14, you are right!
Let's plug (1, 14) into the equation and see what we get: 

*Plug in 1 for x and 14 for y

Answer/Discussion
to 3b
y = 5 ; (2, 5),
(5, 1), (0, 5) 
Let's start with the ordered pair (2, 5).
Which number is the x value and which one
is the y value? If you said x = 2 and y = 5, you are correct!
Let's plug (2, 5) into the equation and see what we get: 
This is a TRUE statement, so (2, 5) is a solution to the equation y = 5.
Now, let's take a look at (5, 1).
Which number is the x value and which one
is the y value? If you said x = 5 and y = 1, you are right!
Let's plug (5, 1) into the equation and see what we get: 
This is a FALSE statement, so (5, 1 ) is NOT a solution to the
equation y = 5.
Now, let's take a look at (0, 5).
Which number is the x value and which one
is the y value? If you said x = 0 and y = 5, you are right!
Let's plug (0, 5) into the equation and see what we get: 
Answer/Discussion
to 4a
; (0,
) and ( , 1) 
In the ordered pair (0, ), is 0 that is given the x or the y value?
If you said x, you are correct.
Plugging in 0 for x into the given equation
and solving for y we get: 

*Plug in 0 for x
*Solve for y

So, the ordered pair (0,  4) would be a solution to the
given equation.
In the ordered pair ( , 1), is the 1 that is given the x or the y value?
If you said y, you are correct.
Plugging in 1 for y into the given equation
and solving for x we get: 

*Plug in 1 for y
*Solve for x

Answer/Discussion
to 5a

Plugging in 0 for x into the given equation
and solving for y we get: 
So, the ordered pair (0, 3/2) would be a solution to the given equation.
Plugging in 1 for x into the given equation
and solving for y we get: 
So, the ordered pair (1, 3/2) would be another solution to the
given equation.
Plugging in 1 for x into the given equation
and solving for y we get: 
So, the ordered pair (1, 3/2) would be another solution to the given
equation.
Filling in the table we get:
(return to problem
5a) 
Last revised on July 29, 2011 by Kim Seward.
All contents copyright (C) 2001  2011, WTAMU and Kim Seward.
All rights reserved.

