Could you help me to solve the following simulaneous equation 4x + 7y = 49, 11x - 5y = 62?

Question

Could you help me to solve the following simulaneous equation
4x + 7y = 49 11x - 5y = 62
If you could give me explanation's as you go that would be great

Answer 1

4x+7y=49 (*5) 20x+35y=245
11x-5y=62 (*7) 77x-35y=434
adding 97x=679 so x=7
sub x=7 in 4x+7y=49
28+7y=49
7y=21 and so y=3
solution set={7,3}

Answer 2

Let:
4x+7y=47 (equation 1)
11x-5y=62(equation 2)

Mutliply (equation 1) by 5 and (equation 2) by 7 to eliminate y.

20x+35y=245
77x-35y=434

Add the two new equations and then solve for x.
20x+35y=245
77x-35y=434
97x =679 (Divide both sides of the equation by 97)
x=7

Substitute the value of x to either equation 1 or equation 2 to solve for the value of y.

4x+7y=47
4(7)+7y=49
28 + 7y=49
28+7y-28=49-28 (by addition property of equality)
7y=21 (divide both sides by seven)
y=3

solution set (7,3)

Check:
Substitute the value of x and the value of y to either equation 1 or equation 2.

4(7) +7(3) = 49
28 + 21 = 49

11(7) - 5(3) = 62
77 - 15 = 62

Answer 3

First you need to separate out x and y, because you can only ever solve an equation with one unknown element.
Therefore, 4x+7y=49 and 11x-5y=62 are your equations.

So lets look at the second equation :

11x - 5y =62
if you re-arrange this so that it equals a number of y's, thus:

11x - 62=5y (note when a number changes sides from left to right of the equal sign it changes from ='ve to -'ve and vice versa.

So if 5y =11x-62

1xy or simply y, has to equal (11x-62) divided by 5.

Now we know a value of y in terms of x's:

y =(11x - 62) / 5

So now you put this value of x into the other equation:

4x + 7y = 49

which means that:

4x + 7 times our y value of (11x-62)/5 = 49

So to put that into an equation I would have :

4x + 7 [(11x - 62)/5] = 49

However I find it hard to work in fractions, so lets get rid of the fraction, by timesing everything by its bottom number (ie 5)

So : 4x times 5 = 20x

7x[(11x-62)/5] times 5 becomes 7 x (11x-62), we just lose the divided by 5.

Not forgetting the 49, which becomes, 245 (49 x 5 = 245)

So lets look at that formula again, we now have:

20x + 7(11x -62) = 245

Lets get rid of the brackets,

20x + 77x - 434 = 245

Wow!! we have everything in x's

So lets move all the x's to one side:

20x + 77x = 245 + 434

So that becomes:

97x = 679

so x = 7 (if you divide each side by 97!)

Now you need to put that value of x back into the other equation, to work out y.

So if we take, 4x + 7y = 49

This becomes :

(4x7) + 7y =49

28 + 7y = 49

Re-arranged equals:

7y = 49 - 28
7y = 21
y = 3
(when you divide each side by 7!)

So what answers did we have?

x = 7 and y = 3,

If you check these in the equations they work out!

4x + 7y = 49
(4x7) + (7x3) =49
28+21=49
49=49

11x-5y=62
(11x7) - (5x3) = 62
77-15 = 62
62=62

Yehaa got there!!

Answer 4

solve one in terms of the variable x then input it for x in the other equation and solve for y then use that y to solve for the x. like this
4x=62+5y :move 5y to other side
x=(62+5y)/4 :divide by 4 on both sides
4((62+5y)/4)+7y=49 :Substitute for x
62+5y+7y=49 :4's cancel out
12y=-13 :combine y terms and move 62
y=-13/12 :answer for y so substitute it in the equation
4x+7(-13/12)=49 :above
4x-91/12=49 :simplify
4x=679/12
x=679/48 or approx. 14.145833333

Answer 5

4x + 7y = 49 ---------1 (x5)
11x - 5y = 62---------2 (x7)

1)make 'y' values the same by multipling equation 1 by 5 and equation 2 by 7=

20x+35y=245
77x-35y=434
------------------
97x =679 <---sutract equations
x =7 (divide both sides by 97)

to get 'y' values substitute x=7 into any equation
eg. 4(7)+7y=49
28+7y=49
7y=21
y=3

Answer 6

4x + 7y = 49
11x - 5y = 62
Multiply the first equation by 5 and the second by 7 to get:
20x + 35y = 245
77x - 35y = 434
Add the above two equations to get:
97x = 679
x = 679/97
plug the above value of x into the very first equation to get
4(679/97) +7y =49
Then y= [49 - 4(679/97)]/7

Answer 7

stake the two equations on top of each other.
4x+7y = 49
11x-5y = 62
you have to change the equations to where if you add them together one of the variables goes away.
so multiply top by 5 and bottom by 7
you get
20x+35y = 245
77x-35y = 434
then 97x = 679
x=7
then plug 7 back into either equation for y
4(7) +7y = 49
28+7y=49
7y=21
y=3

Answer 8

4x + 7y = 49
11x - 5y = 62

multiply 1st eq by 5, and 2nd by 7, to eliminate the y's:

20x + 35y = 245
77x - 35y = 434

97x = 679
x=7

4x + 7y = 49
4*7 +7y = 49
28 +7y = 49
7y = 21
y=3

Answer 9

x=7,y=3

Answer 10

Do your own homework!!! It is ok to ask one for the theory, but it is obvious posting 4 different questions u just need your homework doing!