Download Week 4 Individual Assignment 1 Week 4 Individual Assignment Math

Week 4 Individual Assignment
1
Week 4 Individual Assignment
Math/208
Section 7.1: Exercises 22, 24, 36, 38, 42, 56, and 70
22.
The lines in graph (D) intersect at (2,3) and (2,3) satisfies both equations of the system.
Week 4 Individual Assignment
3x-5y=-9
3(2)-5(3)=-9
10-15=-9
5x-6y=-8
5(2)-6(3)=-8
10-18=-8
Hence Graph D solves this equation
24.
4x+5y=-2
5y=-4x-2
y=-4x/5--2/5
y=-0.8x-0.4
2=-0.8(-3)-0.4
2=2.4-0.4
2=2
4y-x=11
4y=x+11
y=x/4+11/4
y=0.25x+2.75
2=0.25(-3)+2.75
2=-0.75+2.75
2=2
2
Week 4 Individual Assignment
The lines in the graph (a) intersect at (-3,2) and (-3,2) satisfies both equations.
36.
Substitute
y=-3x+19 into y=2x-1.
-3x=19=2x-1
-5x=-20
x=4
Use x=4 in y=2x-1 in order to find out y
y=2(4)-1
y=7
The solution set is {(4,7)}. The equations are separate.
38.
Substitute y=3x into y=-4x-7.
3x=-4x-7
7x=-7
x=-1
Use x=-1 in y-3x in order to find y
y=3(-1)
y=-3
3
Week 4 Individual Assignment
The solution set is {(-1,-3)}. The equations are separate.
42.
Substitute y=x+4 into 3y-5x=6
3(x+4)-5x=6
3x+12-5x=6
-2x+12=6
-2x=-6
X=3
In case x=3, in that case y= 3+4=7. The solution set is {(3,7)} .The equations are
separate.
56.
Write 2x-y=4 as
y=2x-4 and substitute into 2x-y=3
2x-(2x-4)=3
4=3
The equations are not consistent and the solution set is null.
70.
+3y=2
-x+y=1
y=1+x
4
Week 4 Individual Assignment
substitute y=1+x for y in the other equation and solve for x
X+3(1+x)=2
x+3+3x=2
4x+3=2
4x=-1
x = -1/4
substitute x=-1/4 for x in equation and solve for y
-1/4+3y=2
3y=2/1+1/4
3y=8/4+1/4
y=3/4
-1/4+3(3/4)=2
-1/4+9/4=2
8/4=2
2=2
It is independent. {(-1/4,3/4)}
Section 7.2: Exercises 8, 12, 16, 22, 26, 36, and 44
8.
x+y=7
x-y=9
5
Week 4 Individual Assignment
2x=16
x=8
Use x=8 in x+y=7 in order to find out y.
8+y=7
y=-1
The solution set is {(8,-1)}
12.
x-2y=-1
-x+5y=4
3y=3
Y=1
Use y=1 in x-2y=-1
x-2(1)=-1
x=1
16.
In case we multiply the 2nd equation
x-2y=11 by -3, we get -3x+6y=-33.
Add this equation to the 1st equation.
3x+5y=-11
-3x+6y=-33
11y=-44
y=-4
6
Week 4 Individual Assignment
Use y=-4 in 3x+5y=-11
3x+5y(-4)=-11
3x-20=-11
3x=9 x=3
The solution set is {(3,4)}.
22.
Rewrite the 1st equation to suit the type of the 2nd.
2x+y=2
3x+y=-1
Multiply the 1st equation by -1 to get
-2x-y=-2
3x+y=-1
x=-3
Use x=-3 in 2x+y=2 in order to find out y.
2(-3)+y=2
-6+y=2
y=8
26.
Multiply x-y=3 by 6 in order to get
6x-6=18
7
Week 4 Individual Assignment
-6x+6y=17
0=35
The equations are not consistent and the solution set is null.
36.
Multiply both equations by 63.
27x+35y=1701
7x+18y=441
Multiply 1st by -7 and 2nd by 27:
-189x-245y=-11907
189x + 486=11907
241y=0
y=0
7x+18(0)=441
x=63
The solution set is {(63,0)}
44.
Multiply the 1st equation and the 2nd by -12 in order to get the following system.
10(3x-2.5)=10(7.125)
-12(2.5x-3y)=-12(7.3125)
30x-25y=71.25
-30x+36y=-87.75
11y=-16.5
8
Week 4 Individual Assignment
y=1.5
9