sec7_1ism

CHAPTER 7LINEAR EQUATIONS IN TWO VARIABLES

SECTION 1ORDERED PAIRS AND THE RECTANGULAR COORDINATE SYSTEM

1. R, y = 5x / 1; '1+2( s. x- 4y = 3; '3+0('2( 3'1( - 1 '3( ) 2'0( 32 3-1 3)0 = 32 2 'True( 3 3 'True(

V, y 5x / 1; '- 1+-4( Hence+ '- 1+2(and '3+0( are solutions'-4( = 3'-1( -1

-4 -3-1 4. R, 5x /y 4; '1+- 1(-4 - 4 'True( 3'1( - '- 1( = 4

3 ) 1 4s. y 5x / 1; '2+3( 4 = 4 'True(

'3( 3'2( - 13 = 6-1

4; 't+2 (3 5 'False( V, 5x/y

Hence+ '1+2( and '- 1+-4( are solutions 3 't( - '2( 4

2. R, y 2x ) 4; '- 1+3( 1-2 4'3( 2' - 1( ) 4 -1 4 'False(

3 -2)43 2 'False( s. 5x/y 4; '0+- 4(

3'0( - '- 4( = 4V, y 2x ) 4; '0+4( 0)4 4

'4( = 2'0( ) 4 4 = 4 'True(4 0)44 4 'True( Hence+ '1+- 1( and '0+- 4( are solutions

s. y = 2x ) 4; '2+8( 5. R, 5y / 6x = 2; '1+2('8( 2'2( ) 4 3'2( - 4'1( = 2

8 4)4 6-4 28 8 'True( 2 = 2 'True(

Hence+ '0+4( and '2+8( are solutions V, 5y / 6x 2; '- 2+1(3'1(-4'-2( 2

3. R, x ) 4y 3; '1+2( 3)8 = 2'1( ) 2'2( 3 11 2 'False(

1)4 35 3 'False( s. 5y / 6x 2; '!+1 (

V, x- 4y = 3; '- 1+2('- 1( ) 2'2( 3 3'1(-4'!( = 2

-1)4 = 33 3 'True( 3-2 2

1 = 2 'False(

Hence+ '1+2( is a solution

205

Section 1 Ordered Pairs and the Rectangular Coordinate System 207

13. a( p 1o * 2; o = 1y = 3'1( * 2y = 3*2P 5

c( y 3 /4x= x = 0y 3 - 2'0(y 3-0y = 3

The ordered pair '1+5( is a solution The ordered pair '0+3( is a solution

p = 1o) 09 o = - 2 16.p 3'- 2( ) 2 Y(

p = -6)2p 28

The ordered pair '0+2( is a solution

The ordered pair '- 2+- 4( is a solution

14. R, p 2o+19 o = - 1Y 4'-1(-3Y = -4-3Y 2=

/7/x= 1Y x :

5

y - 5 -'i(y = __25 _ 1

5 526 I

Y = -- = - 5-5 5

y / 5 - o9 o = 5y = -5-5P -10

The ordered pair 'i+-5 i}s a solution

V,

The ordered pair '5+- 10( is a solution

1o * 2; o = 03'0( * 20*22

ypyp

c(

V,

The ordered pair '- 1+-7( is a solution


V, p 2o+19 o = 2Y = 4'2( - 3y :/5y 5

c( y = - 5 - o9 o = 0y / 5-0y -5





x = 3

x = 4

x = - 2

4;a 8= 8

29

5x * y 6=3'0( * Y = 4

J)p = 4y 4

5x * Y3'3( * y

7)py

5x * Y = 4;1'+0()p 2

+4)p = 4Y 10

c(

V,

The ordered pair '- 2+10( is a solution


R,17.

p = 2o+19 o : 0p = 4'0( - 3p 0-3p 27

p 1 +0o9 o ? 3p = 3 - 2'3(p 3-6p = 27

p 1+0o9 o:+2y = 3 - 2'- 4(0y 3 * 8p = 11

V,

c(

R,15.


Section 1 Ordered Pairs GJI the Rectangular Coordinate System 64J


V, 4x / 5y = 1; x = -42'- 4( - 5y 1

- 8 - 5y 1/5y 9

y 27

The ordered pair '- 4+- 3( is a solution26.

[(

Y(

y * 1 = 0;Y = -1

y / 4 = 0;y = 4

x a 4

x = 1


The ordered pair '1+4( is a solution[( 4x / 5y2'0( - 5y

e - 5y :/5y

Y

1«+111

13

x a 4V, y / 4 = 0;

Y = 4x = 2

The ordered pair '0+- i( is a solution[( y / 4 = 0;

y = 4x = 0

23. R, y = 5; x a 1The ordered pair '0+4( is a solution


V, y = 5; x = -6

27. R, xxxx

0p) 192'1( * 32*35

p a 1

The ordered pair '- 6+5( is a solution The ordered pair '5+1( is a solution

The ordered pair '0.5( is a solution

24.

[(

R,

y = 5;

y = -4;

x = 0

x = - 5

V, x = 0p) 19 y = - 2x 2'- 2( * 3x = -4*3x 25

The ordered pair '- 5+-4( is a solution The ordered pair '- 1+-2( is a solution

The ordered pair '- 4+- 4( is a solution


25.

V,

[(

R,

p = -4;

y = -4;

y * 1 = 0;Y = -1

o = -4

o = 0

x a =

[( x = 0p) 19 p = +0x 2'0( * 3x = 0*3x = 3


28. R, x / 5y * 1; y = -1x = -3'-1(*1x 3 * 1x = 4

The ordered pair '7+- 1( is a solution The ordered pair '4+- 1( is a solution

The ordered pair ' - i+-1 ( is a solution

V, p)e

y

0;-1

3x = --5

V, x = / 5y * 1; y ? 2x - 3'2( * 1x = -6*1x 29




34. Given c :; 2x * 20

Y( c :; 430430 :; 2x ) 20410 :; 2x205 = x

Z( y = 0o

-240120

240 - 2x-2xx

240 - 2x26~


Z( c = 700700 :; 2x ) 20680 :; 2x340 = x

The ordered pair '340+700( is a solution 37.

c( p = 210210-30 =

15 = x


Given p = 1o) 0.

[( c = 1+4001400 = 2x ) 201380 = 2x690 a x

Y( o : epy ?y

3'0( * 200)2064

The ordered pair '690+1400( is a solution The ordered pair '0+20( is a solution

Given y = 240 - 2x


35.

Y( o : 2SP ?Y

240 - 2'2(240 - 4236

Z( x = 5py ?y

3'5( * 2015 * 2035




Given y = 240 - 2x

V, x : 12Y =Y =Y

3'3( * 209* 206J

5x * 205xx

5x * 201ox

c( x : 3YY =Y =

Z( y = 23233 =1

Y( y = 2626 =6 =2


Given p = 1o) 0.



38.

240 - 2'12(240 - 24216

240 - 2'0(240 - 0240

240 - 2x/4xx

epp ?p

Y( p = 200200 =-40 =

20 :;

[( o :

36.



64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

76.

77.

78.

79.

80.

I '7+0(

J '5+- 5(

I '0+0(

'- 2+- 5( lies in Quadrant III

'4+- 1( lies in Quadrant IV

'5+3( lies in Quadrant I

'- 7+-9( lies in Quadrant III

'!&-4 ( lies in Quadrant IV

' - ~+ 7 ( lies in Quadrant IT

' -~+-i( lies in Quadrant ill

'~+ - ~( lies in Quadrant IV

'5+- 14( lies in Quadrant IV

'- 3+- 3( lies in Quadrant III

a( If x > 0 and y < 0+the point 'o*p( liesin quadrant IV

b( If x < 0 and y > 0+the point 'o*p( liesin quadrant IT

c( If x < 0 and y < 0+the point 'o*p( liesin quadrant III

d( If x > 0 and y > 0+the point 'o*p( liesin quadrant I

The value of x for any point on the y-axisis 4The value of y for any point on the x-axisis 0

The abscissa for point A is 1The abscissa for point C is - 2The abscissa for point E is - 4The abscissa for point G is - 5The abscissa for point I is 7The abscissa for point K is 0

81.

82.

83.

84.

The ordinate for point B is - 1The ordinate for point D is 6The ordinate for point F is - 6The ordinate for point H is 4The ordinate for point J is - 5

The five points chosen are '- 3+- 5(+'- 3+- 3(+'- 3+0(+'- 3+3( and '- 3+5(. Theresulting figure is a vertical line.

y

5«

~----5-)--)---~5-&" x

29

The five points chosen are '- 5+4(+'- 3+4(+'0+4(+ '3+4( and '5+4(. The resultingfigure is a horizontal line. See graphabove.

The five points chosen are '- 5+- 5(+'- 3+- 3(+'0+0(+'3+3( and '5+5(. Theresulting figure is a line through the originthat lies in Quadrants I and III.

y

x

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