I need help and im Lost
2. A system of equations is given below.
2x + 7y = 1
-3x – 4y = 5
1. Create an equivalent system of equations by replacing the first equation by multiplying the first equation by an integer other than 1, and adding it to the second equation.
2. Use any method to solve the equivalent system of equations (the new first equation with the original second equation).
3. Prove that the solution for the equivalent system is the same as the solution for the original system of equations.

Question

I need help and im Lost
2.	A system of equations is given below.
2x + 7y = 1
-3x – 4y = 5
1.	Create an equivalent system of equations by replacing the first equation by multiplying the first equation by an integer other than 1, and adding it to the second equation.
2.	Use any method to solve the equivalent system of equations (the new first equation with the original second equation).
3.	Prove that the solution for the equivalent system is the same as the solution for the original system of equations.

jolo_yolo · Answer

@ganeshie8 @phi

phi · Answer

multiplying the first equation by an integer other than 1

if you have an equation like
x + 2y= 7
and you multiply it by , for example, 7
that means multiply both sides by 7:
7(x+2y) = 7*7
which involves multiplying *every* term on both sides
you would get
7x+14y=49

can you pick a number bigger than 1 ?

jolo_yolo · Answer

8 - can i use that?

phi · Answer

yes, any number you like.

now multiply 8 times the first equation
2x + 7y = 1

jolo_yolo · Answer

16x + 56y = 256 ?

phi · Answer

ok, on the left side. the right side is 8*1

phi · Answer

8*(2x + 7y )  = 8*1

phi · Answer

and that is
16x +56y = 8

phi · Answer

we did this part:
multiplying the first equation by an integer other than 1

ok so far?

now we do this part:
adding it to the second equation.

that means add
16x +56y = 8 
and
-3x – 4y = 5

phi · Answer

16x+ 56y =8
-3x  -  4y = 5

phi · Answer

add the "x's"    16 x take away 3 x's  , gives how many x's
do the same for y's
and then the 8 + 5

jolo_yolo · Answer

wait so i take out the variables and add 8 by 5?

phi · Answer

we add the 2 equations
16x+ 56y =8 
-3x - 4y = 5

can you add them ?

phi · Answer

you add the Left side and you add the right sides

jolo_yolo · Answer

okay ill try

jolo_yolo · Answer

sorry my page was disconnected. would it be 13 + 60y = 13 ?

phi · Answer

16x+ 56y =8 
-3x - 4y = 5

now added together:
16x-3x + 56y - 4y = 8+5

can you simplify that ?

phi · Answer

you are close, but not accurate  ... to solve these we have to be careful with the signs

jolo_yolo · Answer

19x + 52y = 13 ..right?

phi · Answer

16x-3x is not 19x  .  the rest is correct

jolo_yolo · Answer

ayee so 13x

phi · Answer

yes. so the "new" first equation is 13x+52y= 13
 and the second equation is still -3x-4y= 5

jolo_yolo · Answer

oh okay ty, can u help with part 2 n 3?

phi · Answer

to solve
13x+52y= 13
-3x-4y= 5

I would first simplify the first equation.  Do you see a number that divides evenly into 13, 52 and 13 ?

jolo_yolo · Answer

52 divided by 2 is 26 but nothing for 13

phi · Answer

what is 52/4 ?

jolo_yolo · Answer

13 .~.

phi · Answer

so the idea is multiply the first equation by 1/13
(i.e. divide each term by 13).  can you do that ?

jolo_yolo · Answer

so 1/3 * 13x + 52y = 13 ?

phi · Answer

1/13  not 1/3
and we do that to *both sides*  and *all terms*

jolo_yolo · Answer

sorry it was a typo. and ill try to do it

jolo_yolo · Answer

13x + 52y x 1/13 = 5.30  || 13 x 1/13 = 0.99

phi · Answer

like this:
$$ \frac{1}{13} \cdot 13x +\frac{1}{13} \cdot 52y = \frac{1}{13} \cdot 13 $$

think:   13 divided into the "number" part

phi · Answer

13 x  /  13   is x  (because 13 divided by itself is 1)

phi · Answer

what is 52 y / 13 ?

jolo_yolo · Answer

4y?

phi · Answer

yes

phi · Answer

can you write down the simplified version
$$ \frac{1}{13} \cdot 13x +\frac{1}{13} \cdot 52y = \frac{1}{13} \cdot 13 $$?

phi · Answer

the first term is 13 x divided by 13
the second term is 52 y divided by 13
the right hand side (of the = sign) is 13 divided by itself

jolo_yolo · Answer

i got 1x + 4y = 1

phi · Answer

yes.  and most times we don't bother to write 1x, we write x  (but 1x and x mean the samething)

to review, we are solving
13x+52y= 13 
-3x-4y= 5

we simplified the first equation (by multiplying it by 1/13).  we now have
1x + 4y = 1
-3x -4y= 5

what do we get if we add these equations together  (be careful of the + and - signs)
?

jolo_yolo · Answer

-2x -4y = 6

phi · Answer

1x -3x +4y -4y =1+5

-2x   +     ?    = 6

you did the y part wrong.  but the rest is ok.  can you re-do the y 's ?

phi · Answer

4 y's take away 4 y's

jolo_yolo · Answer

4 + -4 = 0y

phi · Answer

yes,  that means 
when we add these equations:
1x + 4y = 1 
-3x -4y= 5
we get
-2x +0 = 6
or just
-2x = 6

now divide both sides by -2 to "solve for x"

jolo_yolo · Answer

x = -3?

phi · Answer

yes
now use 
1x + 4y = 1 
with x=-3 
to find y

phi · Answer

1x+4y= 1
1*-3 + 4y= 1
-3 + 4y= 1
add +3 to both sides

phi · Answer

4y=4
divide both sides by 4
y= 1

phi · Answer

for part 3,  use x=-3  and y=1  in the original equations
2x + 7y = 1 
-3x – 4y = 5

and show that both are true.

jolo_yolo · Answer

Okay, thanks for all your help! much appreciation~