Please help me with my algebra homework?

Question

I need help with this problem:graphical method

Find two numbers such that twice the smaller plus three times the larger is 34, and 5 times the smaller minus twice the larger is 9.

Find two numbers such that 5 times the larger plus three times the smaller is 47, and four times the larger minus the smaller is 20.

Thanks for your help! 10 points for best answer

Answer 1

Let A and B be the two numbers and let B be smaller and A be the larger number.
Twice the smaller is 2B and three times the larger is 3A when they are added give 34
i.e. 2B+3A=34.........................(i)
Again when twice the larger i.e. 2A is subtracted from 5 times the smaller ie 5B, the difference is 9
i.e. 5B-2A=9...........................(ii)
Multiplying equation (i) by 5 and equation (ii) by 2
10B+15A=170.........................(iii)
10B-4A=18...............................(iv)
Subtracting (iv) from (iii)
19A=152
or A=8
By putting this value of A = 8 in any of the above equations, you will get B = 5
So A=8 and B=5 is the answer to your first question.

Same pattern for solving the other question.
5A+3B=47
and 4A-B=20
The equations do not give any solution in whole numbers. the solution is in fractions or there is some mistake in your statement.

Answer 2

Your First question:
Smaller number: x, bigger number: y
From the question: 2x + 3y = 34
5x - 2y = 9
=>Make y the subject : 3y = 34 - 2x (1)
2y = 5x - 9 (2)
(1)=> If x = 1 => y = 10.67
If x = 2 => y = 10
If x = 3 => y = 9.3
If x = 4 => y = 8.67
We then have (1;10.67), (2;10), (3;9.3), (4;8.67), you plot these points on the graph, then join them all together. It should be a straight negative line.

(2)=> If x = 1 => y = -2
If x = 2 => y = 1.5
If x = 3 => y = 3
If x = 4 => y = 5.5
We then have (1;-2), (2;1.5), (3;3), (4;5.5), you plot these points on the graph, then join them all together. It should be a straight positive line.

The bisector of these two lines will give you the approximate values of x and y.

Just do this method similar to your second question.

Answer 3

2s + 3b = 34
5s -- 2b = 9
or
4s + 6b = 68
15s -- 6b = 27
adding
19s = 95 => s = 5 then
2(5) + 3b = 34 => 3b = 24 => b = 8
bigger = 8, smaller = 5 Answers.

5b + 3s = 47
4b -- 2s = 20 , some correction is there.as minus twice the smaller is 20.
or
10b + 6s = 94
12b --6s = 60
adding
22b = 154 => b = 7 then
5(7) + 3s = 47 => 3s = 12 => s = 4
smaller = 4, bigger = 7

Answer 4

Let the smaller number be x and the bigger number be y.

2x + 3y = 34
5x - 2y = 9

Now change the subject to y.

3y = 34 - 2x
y = (34/3) - (2/3)x

5x = 9 + 2y
2y = 5x - 9
y = (5/2)x - (9/2)

Now use both equations of y to find x.


(5/2)x - (9/2) = (34/3) - (2/3)x
(5/2)x + (2/3)x = (34/3) + (9/2)
(19/6)x = 95/6
x = 5
y = (5/2)(5) - (9/2) = 8

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Let the smaller number b x and the larger number be y.
5y + 3x = 47
4y - x = 20
Again, change subject to y.
5y = 47 - 3x
y = (47/5) - (3/5)x

4y = 20 + x
y = 5 + (1/4)x
Using both equations of y, find x.
(47/5) - (3/5)x = 5 + (1/4)x
(47/5) - 5 = (1/4)x + (3/5)x
(17/20)x = 22/5
x = 88/17
y = 5 + (1/4)(88/17) = 107/17

Answer 5

let smaller be x
let larger be y

2x + 3y = 34 (1)

5x - 2y = 9 (2)

(2) can be written as..

2y = 5x - 9
y = (5x - 9) / 2

substitute into (1)

5x + 3.(5x - 9) / 2 = 34

10x + 15x - 27 = 68
25x = 95
x=95/25
x=19/5

substitute back into (2)
y = (5(19/5) - 9) / 2
= 19- 9 / 2
=29/2

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Go ahead, try the second part yourself..This is how you do it.

Let x be the smaller, and y be the larger. The part before the comma is your first equation, and the part after the comma is your second.

Get one variable on one side in one of the equations, and then substitute it into the other equation to solve one variable.

You can then substitute that one back into any one of the original equations to solve the other variable.

Answer 6

If x is the smaller and y is the bigger,

2x+ 3y = 34
5x + 2y = 9.

Draw the above two lines on the same graph and your answer will be the (x,y) coordinate where the two lines intersect (where they cross).

Similar for the other question.
5y + 3 x + 47
4y - x = 20.

Answer 7

1, 2x+3y=34> eq 1
5x-2y=9 >eq2

xing eq1 with 2 4x+6y=68
xing eq2 with 3 15x-6y = 27
therefore 19x= 95
x=5
substitute x = 5 in eq 1
10+3y=34
y=8

2. 5x+3y=47
4x-2y=20

xing eq1 with 2 10x+6y=94
xing eq2 with 3 12x-6y=60
22x= 154
x=7
substitute x=7 in eq 2 4x-2y=20
28-2y=20
-2y=-8
y=4

Answer 8

Question 1
2x + 3y = 34
5x - 2y = 9

4x + 6y = 68
15x - 6y = 27------ADD

19x = 95
x = 5

10 + 3y = 34
3y = 24
y = 8

x = 5 , y = 8

Question 2
5x + 3y = 47
4x - y = 20

5x + 3y = 47
12x - 3y = 60-----ADD

17x = 107
x = 107/17

y = 4x - 20
y = 428/17 - 340/17
y = 88/17

x = 107/17 , y = 88/17

Answer 9

2

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