Algebra Equation Example Help..?

These are to be solved simultaneously, so i will try and take you through it step-by-step - email me if you are stuck:

1) Take the two equations and label them Equation 1 and Equation 2

2) Make sure there is a like term within the equations, and there is, as they both feature 5y

3) Add Equation 1 to Equation 2, and work it out as follows:

(-2x - 5y) + (-5x + 5y) = -43 + -20

-2x - 5y + -5x + 5y = -63

-2x - 5x = -63

-7x = -63

Therefore 7x = 63 (in the positive)

So x must be 9

x = 9

4) Now we use the substitution method to fin the other value, in this case we found x first so now we solve y:

Substitute x = 9 in Equation 1

-5x + 5y = -20

-(5 x 9) + 5y = -20

-45 + 5y = -20

5y = 25

y = 5

There are several ways to solve this problem, but the easiest way would be by adding the quantities in the two equations:

-5x + 5y = -20

+ -2x - 5y = -43

_________________

-7x = -63

x = 9

now, substitute 9 with x for one of the equations and solve for y:

-5(9) + 5y = -20

5y = 25

y = 5

you could also solve this problem through substitution of the variables by first isolation one of the variables and then plugging it into the second equation:

-5x + 5y = -20

-5x = -5y - 20

x = y + 4

so:

-2(y+4) - 5y = -43

-2y - 8 - 5y = -43

-7y = -35

y = 5

and since x = y + 4

x = 5 + 4 = 9

these are the two simplest methods for solving such problems.

The simplest way to solve these simultaneous equations is by the method of elimination. You just add the two equations together, and you eliminate y:

-5x + 5y = - 20

add

-2x - 5y = - 43

_______________

-7x = -63, so

x = 9.

Now you substitute x = 9 into one of the two equations to find y. I`ll use -5x + 5y = - 20, so:

-5*9 + 5y = -20, so

-45 + 5y = -20, so

5y = 25, so

y = 5.

There are various other methods to solve simultaneous equations: this is just the simplest method for solving this particular one.

Hope this helps, Twiggy.

There are many ways of doing this but I will show you a method called system of equations

You have to manipulate each equation so that one of the variables cancel out.

In this case, however, you don't need to manipulate anything because the Y's will cancel out if you add the equations together

(-5x + 5y = -20)

+(-2x - 5y = -43)

----------------------- The Y's cancel

-7x = -63

x = 9

Now plug this answer back in to one of the original equations:

-5(9) + 5y=-20

5y = 25

y = 5

What I did is called the elimination method.

it is faster in this problem.

-5x + 5y = -20

-2x - 5y = -43

add both equations and since +5y and -5y are opposite reciprocals of each other they cancel out so you are left with

-7x = -63

then divide -7 to both sides to leave the X by itself

and you get x= 9

then chose one of the two equations and substitute 7 for X to get the Y value.

ex: -2x -5y= -43

-2(9) -5y= -43

-18 -5y= -43

+18 +18

-5y= -25

then divide -5 into -25 to get the Y value

and -25/-5 = 5

so y=5 and x=9

you can use the addition method, which is basicly just adding or subtracting both of the equations together. the nice thing about this one is that you do not need to rewrite it. so for this one, you would add the top to the bottom, and you go by each term, so the first term would be -5x+-2x=-7x, the next would be 5y+-5y=0(that is the point of the addition method, to eliminate one of the variables), and then the final one would be -20+-43=63. so the final equation would be: -7x=-63. multilpy both sides by -1 to get 7x=63, then divide both sides by 7 to get x=9. then al you have to do is plug the nine into one of the problems(pick the easier one) so you would get -2(9)-5y=-43, then you remove (), so you get -18-5y=-43. add 18 to both sides, -5y=-25, then mulitply both sides by -1, 5y=25, then divide both sides by 5: y=5. there you go!

Add the two equations together.

-7x + 0y = -63

x= 9

Substitute for x in the first equation:

-45 + 5y = -20

5y = 25

y = 5

solve both the equations .. (adding the 2 equations:

-5x+5y=-20

-2x-5y=-43

-------------------

-7x =-63 (as +5y-5y=0)

7x= 63 ( cancelling minus sign both sides)

x=63/7 ; therefore x=9

now substitute x value in any of the above 2 equations......i am doing it in 1st eq-

-5(9)+5y=-20

-45+5y=-20 ; 5y=-20+45 ; 5y=25 ; y = 25/5 ; so y=5

thats how we get x=9 and y=5

start by solving for x:

-5x+5y=-20

-2x-5y=-43

+5y-5y cancel out so...:

-5x=-20

-2x=-43

add -5x and -2x and that gives you -7x ....and add -20 and -43 and you get -63 ... so:

-7x=-63

divide both sides by -7 to get x by itself...:

since both numbers are negative and two negatives make a positive the answer is 9

now to find y use the first equation and substitute 9 for x ...:

-5(9) +5y =-20

45+5y=-20

move 45 to the other side to get y on one side:

5y= 25

divide both sides by 5 and you get y=5

you add the top and the bottom b/c the y cancels out

-5x + 5y = -20

+ -2x + -5y = -43

_____________

-7x + 0y = -63

-7x = -63

x = 9

Now you just plug in 9 into one of the above equations

-5*(9) + 5y = -20

-45 + 5y = -20

5y = 25

y = 5

Hope this helps