Hi. Can someone please help me solve this question? Given the simultaneous equations: {3x+4y=-3, 5x=2y+19} (a) Write the equations in the form AX=B, where, A, X andB are matrices. (b) Determine A-1 (that's inverse; -1). (c) Calculate A-1<-- (inverse) B (d) Hence, solve for x and y.

Use matrices to solve the system of equation. {x+2y=-4, 2x+y=1}

solution: (2,-3)

The sum of two numbers is 41, and their difference is 11. What are the two numbers?

1) n+m=14
2) n-m=11
adding 1) and 2)...
2n=25
n=25/2

m=14-25/2=3/2

One number is 5 greater than another number. their sum is equal to 5 times their difference. Find the numbers.

1)x=y+5
2)x+y=5(x-y)

1) tells us x-y=5
therefore we can repalce x-y with 5 in 2)

new system:

x+y=25
x-y=5 

adding the two equations...

2x=30

x=15
so...

y=10

Solve: {y=1/2x-3; 4x-2y=16}

4x-2(1/2x-3)=16
4x-x+6=16
3x=10
x=10/3

y=
1/2(10/3)-3(3/3)=
5/3-9/3=
-4/3
Solution:
(10/3, -4/3)

Solve the system: {15x - 9y = 0; 2x + 3y = 21}

from (1)...
y=5/3 x

from (2)...
2x+3(5/3 x) = 21
2x+5x=21
7x=21
x=3

then
y=5/3 (3)
y=5
solution:
(3,5)

Solve the system: {x=y+2; 2y=x-1}

using (1) substituted into (2)...
2y=(y+2)-1
2y=y+1
y=1

then
x=1+2
x=3

solution:
(3,1)

What is the solution of the system? Use substitution {-4y-3x=-11, x-2y=17}

2)
x=2y+17
1)
4y+3(2y+17)=11
10y+51=11
10y=-40
y=-4

x=2(-4)+17=9
solution: (9,-4)

A math test has 25 problems. Some problems are worth 2 points and some are worth 3 points and the total for the test is 66. How many 2 points and 3 points promblems are there.

x-->2pt questions
y-->3pt questions

1)  x+y=25  <--- total questions
2)  2x+3y=66 <--- total points

Using substitution:
2x+3(25-x)=66
2x+75-3x=66
75-66=x
x=9 
y=25-9=16 
there are 9 - 2pt problems and 16 - 3pt problems

Solve by substitution: {6x+2y=11, 4x+y=6}.

6x+2(6-4x)=11
6x+12-8x=11
-2x=-1
x=1/2
y=6-4(1/2)=6-2=4
y=4
solution: (1/2, 4)

Martha is 1 year older than twice his sisters age. The difference of their ages is 8. Find their present ages.

1) M=2S+1
2) M-S=8
setting the equations up to solve...
M-2S=1
-M+S=-8

-S=-7
S=7
M=2(7)+1=15 

9) Chose A, B, or C from the list below. {4x+2y=8, Y=4-2x } A) Inconsistent B) Consistent & Dependent C) Consistent & Independent

If we add 2x to both sides of the lower equation then double each of it's terms we'll get the upper equation. These lines both have the same solution, so the system is consistent and dependent.

:)

9) Chose A, B, or C from the list below. 4x+2y=8 Y=4-2x A) Inconsistent B) Consistent & Dependent C) Consistent & Independent

If we add 2x to both sides of the lower equation then double each of it's terms we'll get the upper equation. These lines both have the same solution, so the system is consistent and dependent.

:)

A larger number is two less than four times a smaller. If the sum of the numbers is 18. Find the number

1) l=4s-2
2) l+s=18

subtracting 1) from 2)...
s=18-4s+2
5s=20
s=4
therefore l=14

A change purse contains 120 coins worth $10.They are all nickels and dimes.How many of each coins are there?

(1) n+d=120 <- number of coins
(2) 5n+10d=10(100) <- amount of money 


5*(1) gives us...
5n+5d=600 


(2) -  5 * (1) gives us...
10d-5d=400
5d=400
d=80 
80 dimes and 40 nickels 

twice a number added to a second number is 45. the sum of the two numbers is 32. Find the numbers

System:

1) 2m+n=45
2) m+n=32

subtracting equations...
m=12 

so n=20

Solve: -5x+12y=21, x-2y=-5

-5x+12y=21
1x-2y=-5
-5x12y=21
5x-10y=-25
2y=-4
y=-2


x-2(-2)=-5
x=-5-4
x=-9

The number of men in a tour group is 15 times the number of women. If there are 48 people in the group, how many are men?

System:
1) x+y=48
2) x=15y 



Solution...
(15y)+y=48
y=3 


x=15*3=45 
45 men

separate 30 into two parts such that the larger is 6 less than twice the smaller. find the working equation of this and the answer.

1) 2x-6=y
2) x+y=30 

then we write... 
x+(2x-6)=30
3x=36
x=12 



and so y=18

solve: 1) 3x+y=17, 2) 4x-y=18

1) 3x+y=17
2) 4x-y=18 

adding the two equations yields:
7x=35


thus
x=5 



now we can find y...
3*5+y=17
y=2