Can you help me to solve the following simultaneous equation's 5x + 3y = 52 and 7x + 11y = 100?

Question

Can you help me to solve the following simultaneous equation's
5x + 3y = 52 and 7x + 11y = 100
11x + 8y = 62 and 23x + 12y = 106
2x - 5y = 62 and 7x - 3y = 60
15x - 19y =22 and 20 x - 23 y = 34
4x + 7y = 49 and 11x - 5y =62
7x + 6y = 72 and 9x - 8y = 14
If you can give me step by step explanation's as you go that would be great. Thankyou

Answer 1

I'll solve the first for you so that you can learn, but you need to practice by doing the others. They are pretty much all the same thing, but with different numbers.

Lets look at the first prob:

1) We need to get rid of a variable so that we can solve for the other. We'll get rid of ' x ' first by multiplying each equation by a number that will make the x's opposite.

5x + 3y = 52 --> * 7
7x + 11y = 100 --> * -5

2) By multiplying the entire first equation by 7, we now have a 35 x. By multiplying the entire second equation by -5, we now have a -35x. We can now cancel out the x's, because " 35x - 35x = 0 ", obviously.

35x + 21y = 364
-35x - 55y = -500

3) Now we are going to add the two equations together, so that we can solve for a ' y ' that agrees with both equations.

21y = 364
-55y = -500

4) " 21y -55y = -34y " and " 364 - 500 = -136 ." Now we can solve.

-34y = -136

5) We are going to use this value and plug it back into one of our initial equations to find ' x '

y = 4

6) I chose the first equation, although you can use either. Solve for x.

5x + 3(4) = 52

7)
5x = 40

8)
x = 8

Now we have our final solution!
x = 8 and y = 4

I hope this helps you :D

Answer 2

Here's what you do: Let's look at the equations together. 5x + y = - 7 7x - 3y = - 45 Here's the deal...you can't solve an equation that has two variables UNLESS you can eliminate one of the variables. I'm going to take the first equation and multiply it all by 3. This will cause the middle y term to become a 3y...you'll see why in a second. 3(5x + y = - 7) 7x - 3y = - 45 Now distibute the three... 15x + 3y = - 21 7x - 3y = - 45 Now you can see that if you combine the two equations, the "y" term will be eliminated. (That's why this method is called the Elimination Method.) So let's combine all like terms (the 15x with the 7x, the -21 with the -45). 22x + 0 = - 66 Now I think you can solve the equation and tell me what the value of x is. 22x = - 66 x = - 3 YAY!!! But wait...there's more...we still have to find the value of y. Now that you have x, just "plug" it into any of the original equations to find y. 5x + y = -7 5(-3) + y = - 7 - 15 + y = - 7 ...add 15 on both sides of the equal sign... y = 8 YAY!!! Now you have your solution...(-3, 8).

Answer 3

First step:
You solve the first one equation to find x. 5x + 3y = 52 => x = (52-3y)/5
Second step:
You place (52-3y)/5 in the second equation where is x:
7x + 11y = 100 => 7*[(52-3y)/5] + 11y = 100.
Third step:
Now you have an equation with only one variable (y), so you solve the equation to find y. Therefore you find y.
Final step:
Place the value of y (the number you found) in the first equation and you have an equation with only one variable (x). So solve the equation and find x.

This is a timespendind method, but the most safe.
There are as far as I know another two methods.
1) to make the equation have exactly equal x (by multiplying one of them) and then subtrack them
2) by using a table with the numbers before x and y (5,3 7,11)

I believe you go with the first method first to get some experience and then check the other methods with help from some other person (physically if possible)

Answer 4

5x + 3y = 52

7x + 11y = 100

- - - - - - - - - - - - - - - - - - -

The Elimination by addition Method

7(5x) + 7(3y) = 7(52)

-5(7x) + (-5)(11Y) = -5(100)
- - - - - - - - - - - - - - - - -

35x + 21y = 364

-35x - 55Y = - 500

- - - - - - - - - - - - - - - - -

- 34y = - 136

- 34y/- 34 = - 136/- 34

y = 4

The answer is y = 4

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - - - -

Solving for x

5x + 3y = 52

5x + 3(4) = 52

5x + 12 = 52

5x + 12 - 12 = 52 - 12

5x = 40

5x/5 = 40/5

x = 8

The answer is x = 8

Insert the x value into equatiion 1

- - - - - - - - - - - - - - - - - - - -

Check for equation 1

5x + 3y = 52

5(8) + 3(4) = 52

40 + 12 = 52

52 = 52

- - -- - - - - - - - - - - - - - - -

Check for equation 2

7x + 11y = 100

7(8) + 11(4) = 100

56 + 44 = 100

100 = 100

- - - - - - - - - - - - - - - - - - - - - - - -

The solution set is { 4, 8 }

Answer 5

5x + 3y = 52
7x + 11y = 100
35x + 21y = 364 (multiply 1st equation by 7)
35x + 55y = 500 (multiply 2nd equation by 5)
.........34y = 136 (subtract 1st equation from 2nd)
.............y = 136/34 (divide both sides by 34)
y=4
5x + 3*4 = 52 (substitute 4 for y in 1st equation)
5x + 12 = 52
5x = 52 - 12
5x = 40
x = 8
(x,y) = (8,4)

The rest can be solved using the same method.

Answer 6

5x+3y=52 & 7x+11y=100
Step 1:
5x+3y=52} multiplied by 7
7x+11y=100} multiplied by 5

Step2:
35x+21y=364
35x+55y=500

Step 3:
Change the signs:
35x+21y=364
35x+55y=500
- - -
-------------------------

-34y=-136
34y=136
y=136/34
y=4 Answer


Solve the other questions accordingly

Best of luck to u.

Answer 7

I will solve the last on
"7x + 6y = 72 and 9x - 8y =14"
at first for equsion 1
7x + 6y = 72 we get

" x = (72 - 6y ) /7 = 10.2857 - 0.857y" now we susbtetute in 2


9*(10.2857 - 0.857y) - 8y = 14
92.571- 7.713y - 8y = 14


y= (92.571- 14 )/ 15.713 = 5

and x= 6

Answer 8

1/) 5x+3y=52---x=52-3y/5
7x+11y=100---x=100-11y/7

substitution--x=x
7(52-3y)=5(100-11y)
364-21y=500-55y
55y-21y=500-364
34y=136
y=136/34
y=4

x=100-11y
therefore x=100-44/7
x=56/7
x=8

others are solved like this!