substitution problem.?

Question

how to solve?

-3x-y=2
-6x+2y=-2



and



x+5y=2
x-1=2y

Answer 1

Use one equation to substitute into the other,then solve for a one variable problem. Use your new information (the solved variable) to solve for the second variable.

For the first set:

-3x - y = 2 rearranged becomes:
y = -3x -2

Using this "definition" of y, substitute it into the second equation as such:

-6x + 2(-3x -2) = -2
-6x - 6x - 4 = -2
-12x = 2
x = -1/6

Substitute -(1/6) for x in either equation to solve for y:

-3(-1/6) - y = 2
y = -3/2

Do the same for the second pair of equations to make sure you got it (the answers for x and y are x=9/7, y = 1/7).

Answer 2

QUESTION 1
(1) -3x-y=2
-3x = 2+y

(2) -6x+2y=-2
-6x= -2-2y

Multiply equation (1) by 2:
-3x = 2+y
-6x = 4+2y

Then, equate both equations to each other, since both equals to
-6:
4+2y=-2-2y
4y=-6
y= -(6/4)

Substitute y=-(6/4) into equation (1),
-3x-(-6/4)=2
-3x+(6/4)=2
(6/4)-2=3x
-(1/2)=3x
x=-(1/6)


QUESTION 2
(1)x+5y=2
x=2-5y

(2)x-1=2y
x=2y+1

Equate both equations to each other:
2-5y=2y+1
1=7y
y=1/7

Sub y=1/7, into equation 1:
x+5(1/7)=2
x+5/7=2
x= 9/7

Answer 3

For the first one, all you need to do is isolate one of the variables, and then enter it into the other equation. For your first example

-3x - y = 2
-6x + 2y = -2

Let's isolate the y in the first equation. That'll give us

y = -3x - 2

If we plug this into the second equation, we get

-6x + 2(-3x-2) = -2

Now, we just solve for x.

-6x - 6x - 4 = -2
-12x - 4 = -2
-12x = 2
x = -1/6

To solve for y, we just put x = -1/6 into one of the equations.
-3(-1/6)-y = 2
1/2 - y = 2
y = 1/2 - 2 = -3/2

x = -1/6, y = -3/2

Now you try the same thing for the second one.

Answer 4

1)
in the first equation: y=-3x-2
substitute that into the second equation
-6x+2(-3x-2)=-2
-6x-6x-4=-2
-12x=2
x=-1/6
plug x into either of the original equations
-6(-1/6)+2y=-2
1+2y=-2
y=-3/2
so the solution is (-1/6,-3/2)

use the same method on #2

Answer 5

y=-3x-2 -6x-6x-4=-2 -12x=2 x= -1/6 y= -3/2


x=2-5y 2-5y-1=2y 7y=1 y=1/7 x=9/7

Answer 6

multiply -3x-y=2 by 2, you will get -6x-2y=4

let -6x-2y=4 is equation 1
let -6x+2y=-2 is equation 2

equation 1 plus equation 2
-12x = 2
x = -1/6
substitute x = -1/6 to equation 1, you will get y = -3/2




let x+5y=2 be equation 3
let x-2y=1 be quation 4

equation 3 minus equation 4
7y = 1
y = 1/7

substitute y = 1/7 to equation 3
x = 9/7

Answer 7

To sove by substitution, solve for x in terms of y from one of the equations, put that expression in for x in the other. What you have then is one equation in y which you can solve directly. When you get that value of y, put it into either equation to get x.

Example: in your first set, -3x-y=2, so x = (y-2)/3. Put this in for x in -6x+2y=-2: -6(y-2)/3+2y=-2, etc.