Homework Help

Find the solution to each system of equations by the substitution method.Check...

user profile pic

kim1246 | (Level 3) eNoter

Posted April 11, 2013 at 11:46 AM via web

dislike 1 like

Find the solution to each system of equations by the substitution method.Check answers.write you your solution in the form (x,y),(p,q) or (s,t).           A) 4x-3y= -9   x-y= -3                          

 

B)p+2p-4=0   7p-p-3=0

2 Answers | Add Yours

user profile pic

durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted April 11, 2013 at 12:06 PM (Answer #1)

dislike 1 like

Please note that, interms of eNotes rules, you may only ask one question at a time. Please repost your second question separately. It does not follow the same criteria as A.

Please refer to the attached links to help you with equations:

   1.   `4x-3y = -9`  and    2.   `x-y=-3`

To use the substitution method convert 2. so that it reads x=:

`therefore x-y = -3 ` becomes `x= y-3`

Now substitute this into the other equation instead of x:

`4(y-3) - 3y = -9`

Now there is only one unknown variable (y) :

`4y - 12 -3y= -9`

`therefore 4y - 3y= -9+12`

`therefore y = 3`

Now solve for x by substituting into any one your original equations:

`therefore x=y-3` becomes `x= 3-3`

`therefore x=0`

`therefore (x;y) : (0; 3)`

Now check your answer (there are various methods) by substituting both values into any one of your equations and rendering the left-hand side(LHS) = right-hand side(RHS) :

`4x - 3y = -9` becomes `4(0) - 3(3) = -9`

`therefore 0 - 9 = -9`

`therefore -9 = -9`

Therefore LHS=RHS

(x;y) : (0;3)

 

 

 

Sources:

user profile pic

oldnick | (Level 1) Valedictorian

Posted April 12, 2013 at 2:39 AM (Answer #3)

dislike 0 like

`a)`

`4x-3y= -9`

`x-y=-3`

multiply secon realtion by 3:

`3x-3y=-9`

subtract this one from first:

`4x-3y-(3x-3y)=-9-(-9)`

`4x-3y-3x+3y=-9+9`

`x= 0`

thus:  from the second relation: `-y= -3`    `y=3`

`b)`

`p+2q-4=0`

`7p-q-3 = 0`

multiply second by 2:

`14p-2q-6=0`

add to the first:

`p+2q-4+14p-2q-6=0`

`15p-10= 0`   `15p= 10`   `p=2/3`

From first relation we get:

`2/3 + 2q-4=0`  `2q-10/3=0`   `2q=10/3`  `q= 5/3`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes