what am i doing wrong when i solve these problems?

Question

7x+2y= -1
3x-4y=19
answer: 10x + -2y=18


5x-3y=16
4x+5y= -2
answer: 9x+ -2y= 14


4x+3y=9
3x+4y= 12
answer: 7x+7y=21



3x-5y=7
5x-2y= -1
answer: 8x-3y=6

Answer 1

Solving equations means to figure out what is the solution for the equations, i.e, for what values are the equations true.
For this you need to eliminate one of the variables and then solve for the other.
I will do the first one and you can figure out the rest.

7x+2y= -1 ----------------1
3x-4y=19 ----------------2

Now multiply equation 1 with 2,
therefore equation 1 becomes,

14x + 4y = -2 ------------ lets name it --------3
3x - 4y = 19 -------------2
-----------------------
17x + 0 = 17
now, x = 17/17 = 1
put x=1, in equation ----2
thus,
3(1) - 4y = 19
4y = 3 - 19
= -16
y = -16/4
y = -4
Hence the solution of the two equations is ,
x = 1 and y = -4

You can now figure out what went wrong and solve the others.

Answer 2

I think you're supposed to find where these lines intersect...? (The directions are important, people! Don't just give us equations!) In which case you're going about it a slightly wrong way. I'll do #1 for example.

If 7x + 2y = -1, then that means 14x + 4y = -2 (just multiply both sides by two).
Then add THOSE two equations. the +4y and -4y cancel, leaving 17x=17. That means x=1. Plus this x into either equation to find y. Let's use the first one:
7(1) +2y = -1
7 + 2y = -1
2y = -8
y= -4
So they intersect at the point (1, -4).

#2: multiply both sides of equation 1 by 5, and equation 2 by 3. then the -15y and 15y cancel out, leaving only x again.

#3: multiply either equation by -1 on both sides, then follow advice for #2. Cancel out either x or y and plug it into either equation and solve for the other.

#4: same strategy as #3

Answer 3

Don't just blindly add them together. You have two equations on two variables. In general, that is enough for a solution. Here are the first two as an example.

1) 7x + 2y = -1
so 14x +4y = -2
Now add, canceling out y's:

17x = 17
x = 1
y = -4

2) 5x-3y=16 4x+5y=-2
25x-15y=80 12x+15y=-6

37x=74
x = 2
y=-2

Answer 4

First one, use elimination starting with multiplying the first equation by two and then adding.

14x+4y=-2
plus
3x - 4y=19
equals
17x=17
x=17
Find y by plugging it in to either equation:
3(17)-4y=19
51-4y=19
4y=32
y=8

So, what you are doing wrong is you are just adding the equations together, you want to make it so you can eliminate a variable. Here is the rest more simply:

20x -12y=64 times 4
-20x + 25y = 10 times -5
13y=74 add them together
y=74/13

12x+9y=27 times 3
-12x-16y=-48 times =4
-7y=-21 add them together
y=3

15x-25y=35
-15x+6y=3
-19y=38
y=-2

Remember you find the other variable by plugging the variable you found into the equation, and solving.

Hope this helped

Answer 5

what you did wrong: you didn't solve for anything. -_-

what you should do:

make sure to eliminate one variable by multiplying through by an integer: for the first one...

7x + 2y = -1
3x - 4y = 19

Multiply the first one through by 2: 14x + 4x = -2

add the two equations:

17x = 17
x = 1
y = -4

try to do the rest yourself using this method :) its sorta like finding the common denominator when adding fractions

Answer 6

I don't think you are doing these correct.
you need to shift one of the equations so that you have
for instance, 7x+2y=-1
2y=-1-7x
y=(-1-7x)/2
now plug in this to the 2nd equation....
3x-4[(-1-7x)/2]=19
3x+2 +14x=19
17x=17
x=1 now plug that into either equation and you have 7+2y=-1
so y=-4
try that for the rest! good luck!

Answer 7

the first one is correct
the second should be 9x+2y=14
the third correct
the fourth should be 8x-7y=6

looks like you just made a few addition mistakes

Answer 8

The following three formulae are all equivalent: M/V=D M=VD M/D=V So, to get the volume (in mL), you take the mass (112 grams), and divide by the density (13.6 g/mL). This gives you something around 8.235

Answer 9

all you did was list equations.