Question

solution find x and y
y-x=-13
-4x+3y=-51

Answer 1

Alright, there are two ways you can look at solving a problem like this. You can either go with substitution, or you can go with equation addition.

Have you gone over both? If so, is either more intuitive for you?

Answer 2

oh yeah, my bad its substitution

Answer 3

Alright. Equation addition works just as well, but if you haven't gone over that yet then I wouldn't want to confuse you.

Answer 4

Alright, so the basic principle behind substitution is that you're trying to eliminate a letter by substituting in part of the equation from another part. So we look at this and we see the first equation

y-x=-13

can be very easily manipulated to
y=-13+x

Answer 5

Now this is certainly known to be true. This is a fact and we can take this equality and use it anywhere. Anyplace we see "-13 +x" we can put a y, and anywhere we see a "y" we can put in -13+x

Answer 6

So we look at our second equation
-4x + 3y =-51

and see we can entirely eliminate y by substituting in -13+x wherever it is.

Answer 7

So if we go ahead and try that we have

-4x+3(-13+x) =-51

Answer 8

And from there, it's simple algebra. Do you think you can go through that on your own?

Answer 9

im not sure, would the first step end up being -4x+3-13x=-51?

Answer 10

Umm no. Remember you can always go back to order of operations if need be.

Answer 11

Umm, you're familiar with 3(-13+x) notation right? if you see a number outside that parenthesis that means multiplication

Answer 12

so i multiply 3*-13

Answer 13

So why don't you show me, if the problem were just -4x+3(-13+x) = -51

How would you go about finding x?

Answer 14

If you're multiplying two things, you've got to remember to distribute.

Are you familiar with how to work with parenthesis? Or have you not seen something written like that before?

Answer 15

i have , but a few years ago. im in geometry but i have to get a credit for algebra. and so i forgot how it all really works

Answer 16

Alright that's fair. If having letters thrown in there makes it seem more complicated, you can always take it back to something simpler. That's something I like to do if I'm ever lost.

Like, if you're ever confused about fractions or multiplication rules, just use really simple examples.

Answer 17

So say x is 2

and we want to know what 3(-13+2) is.

Answer 18

-39+6?

Answer 19

If we just say it's -13(3) +2 we end up with -39 +2 = -37

if we multiply everything in the parenthesis we have -13(3) +2(3) = -39 +6 = -33

Answer 20

Right. So you can just double check if you're not sure about multiplication rules

Answer 21

So you want to multiply everything in the parentthesis by 3

Answer 22

So 3(-13+x)
= -13(3) +x(3)

Answer 23

=-39 +3x

Answer 24

-4x+3(-13+x) =-51
-4x -39 +3x =-51

Answer 25

Do you think you can solve it from there?

Answer 26

most likely , but since there are two of the x will i need to add 39 to the other side

Answer 27

Right. So adding 39 to both sides we have ....

-4x -39 +3x +39 = -51 +39

Answer 28

Which you can simplify to
-4x +3x = -12

Answer 29

and then i add -4x and 3x and then divid it by 12?

Answer 30

Let's take it 1 step at a time. First add the -4x and 3x

Answer 31

What should the equation look like now?

Answer 32

-1x=12

Answer 33

That's right. Remember, we are trying to find what x is. Can you see what x is from that?

Answer 34

-12

Answer 35

Oh wait. Close. Small mistake you dropped a negative sign from the -12 earlier.

Answer 36

Scroll up and you'll see the equation was -4x +3x = -12

Answer 37

So the answer is going to be x =12 right?

Answer 38

oh okay so 12

Answer 39

Alright. So we have half the answer, and the next step is super simple. Let's rewrite the problem:

y-x=-13
-4x+3y=-51

and we know that x = 12

Answer 40

Do you see how you can (fairly quickly) find what y is from that?

Answer 41

would it be -1

Answer 42

Right. Perfect.

Answer 43

So then you have your answers

y = -1
x= 12

Answer 44

Just to be sure we can plug these in to each equation to make sure we have the right answer.

Answer 45

-1)-(12)=-13
-1-12 =-13
-13 =-13

which is certainly true

-4(12)+3(-1) = -51
-48 -3 =-51
-51 = -51

Which is certainly true

Answer 46

Do you understand all the steps we took to get to that, or do you want to try another one?

Answer 47

i get it now :)

Answer 48

Alright cool c:

That took a while. If you wanted to show your work concisely it would look something like

-4x+3y=-51
y-x =-13

y= -13+x
Substituting ->
-4x+3(-13+x) =-51
-4x -39 +3x = -51
-x =-12
x=12
Subtituting ->
y-(12) =-13
y=-1

Which only took about a minute or two to type

Answer 49

alright, thank you though