Question

Solve the system by substitution:
-4x-3y=11
x=5y+3

Answer 1

lilig got it

Answer 2

Not sure where to start with this one?

Answer 3

well we already have the second equation which tells us what x is
x = 5y + 3

now we use this in our first equation, so wherever you see x in the first eqation just replace it with what we have here. So the first eqaution is.

-4x - 3y = 11

now we replace x with what we have so we should get

-4(5y + 3) - 3y = 11

now expand the brackets

-4 * 5y = -20y
-4 * 3 = -12

so your equation should look like this now

-20y - 12 - 3y = 11

now bring all the numbers to one side and leave all the variables on the other
remember bringing numbers to the other side will change it to the opposite value.
so bringing a positive to the other side will change it to a negative and vice versa.
e.g. bringing -12 to the other side will give you + 12 or 12

so now the equation will look like this

-20y - 3y = 11 + 12

so we now have

-23y = 23

now to get y on its own and to solve y we divide both sides by the number next to y which is 23

so you would to this

-23y / 23 = 23 / 23

which will give you

-y = 1

and to get a positive y instead of negative y
use just swap sides remembering that bringing something to the other side will change its value from positive to negative or from negative to a positive

so you will now get

-1 = y

now we have worked out what y is we use this to work out what x is

so now we use the first equation again and anywhere where we see y we replace by the figure we have found

so the equation is

-4x - 3y= 11

now repace y with the number we have so it should look like this

-4x - 3(-1) = 11

expand the brackets
so you would do

-3 * -1 = 3

remember - * - equals positive or +

so now the equation will look like this

-4x + 3 = 11

remember bring the numbers to one side and the variables on the other side
so you should now have

-4x = 11 - 3

which is

-4x = 8

now divide both sides by the number next to x to solve x which is 4
so it will look like this

-4x / 4 = 8 / 4

which gives you

-x = 2

now remember we want x to be positive and to do that we just swap both sides around

which will give you

-2 = x

now to check just use the figures in any of the one equations and see if you get the same answer

so

x = 5y + 3

so it will look like this when checking replace y with the answer we already got

x = 5(-1) + 3

so you do

5 * -1 = -5

so you will get

x = -5 + 3

which means

x = -2 which is the same answer we got :)

now try using these values in the first equation
which was

-4x-3y=11

this will now look like

-4(-2) - 3(-1) = 11

so you do

-4 * -2 = 8
-3 * -1 = 3

so it will now look like this

8 + 3 = 11

which is correct and thats how you check your answer and i advise you to always check your answer ( i made a mistake the first time round so this is why it took me so long but it is easy to make a mistake)

dont forget to click good answer :)

Answer 4

Thank you for the time you spent breaking this down!