solve the system of equations: first: 4x-2y=2, second: y= -4x-7?

Question

i need a step by step solution... thanks!

Answer 1

4x - 2y = 2- - - - - - Equation 1
y = - 4x - 7- - - - - - Equation 2
- - - - - - - - - - - - -
Insert the y value of equation 2 into equation 1
- - - - - - - -
4x - 2(- 4x - 7) = 2

4x - (- 8x - 14) = 2

4x + 8x + 14 = 2

12x + 14 = 2

12x + 14 - 14 = 2 - 14

12x = - 12

12x/12 = - 12/12

x = - 1

The anser is x = - 1

Insert the x value into equation 1

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

4x - 2y = 2

4(- 1) - 2y = 2

- 4 - 2y = 2

- 4 - 2y + 4 = 2 + 4

- 2y = 6

- 2y/-2 = 6/- 2

y = - 3

The answer is y = - 3

Insert the y value into equation 1
- - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

4x - 2y = 2

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

- 4 - (- 6) = 2

- 4 + 6 = 2

2 = 2

- - - - - - - - -

Check for equation 2

y = - 4x - 7

- 3 = - 4(- 1) - 7

- 3 = - ( - 4) - 7

- 3 = 4 - 7

- 3 = - 3

- - - - - - - - -

The solution set { - 1, - 3 }

- - - - - - - - - - - - - s-

Answer 2

Step 1: align the equations so they align vertically

4x - 2y = 2
-4x - 1y = 7 (rearranged to get in the same form)


Step 2: see if either variable will be eliminted by adding, if not multiply one equation by a constant so that they will. In this example, we see that the x's will cancel out (4x + -4x = 0)

4x - 2y = 2
-4x - 1y = 7
---------------------
0x - 3y = 9

But what if this wasn't the case? Let's see how we could cancel out the y instead. If we multiply the second equation by -2 we get:

4x - 2y = 2
-4x(-2) - 1y(-2) = 7(-2)

4x - 2y = 2
8x + 2y = -14
-----------------------
12x + 0y = -12

See how that works?

Step 3: solve for the variable

In the first above, we have -3y = 9. -3y/-3 = 9/-3, y = -3

In the second we have 12x = -12, 12x/12 = -12/12, x = -1

Step 4: solve for the second variable by substitution

Normally we would only do one of the variables in step 2, not both... (I only did both to illustrate multiplying a contstant). To solve for the second, you simply substitute your answer in any of the given equations. Since x = -1, let's put it in the first:

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


Alternate method: another way to solve these is to solve one equation for a single variable, then substitute that into the second. For example, we have y = -4x-7, so we can put -4x-7 into the first equation in place of y:

4x - 2y = 2, y = -4x-7
4x -2(-4x-7) = 2
4x + 8x + 14 = 2
12x + 14 - 14 = 2 - 14
12x = -12
12x/12 = -12/12
x = -1

Both methods work well, it just depends on which you prefer (or which your instructor wishes you to use ;) )

Hope this makes sense and is of a help to you! :) Good luck!

Answer 3

-First you nedd to isolate one letter(variable). And you already have that(y=-4x-7).
-Then if you know that y is -4x-7, its just a matter of putting -4x-7 where is y in the other equation, like this.
4x-2(-4x-7)=2.
-Now you need to solve this new big equation, in order to find the value of x.
(first solve the multiplications)
4x + (-2 multiply -4x) (-2 multiply -7) = 2
<=>4x + (+8x) (+14) = 2
<=>4x + 8x +14 = 2
(now put all the x in one side, and all that do not have x in the other side of the = )
<=>4x+8x=2-14(the 14 changed sides so changed from + to -)
<=>12x=-12
<=>x=-(12/12)(you want the x isolated, so what is next(multiplying) to the x goes to the other side of the = but will divide what is already on the other side).
<=>x=-1(you now know that the value of x, but you need the value of all the other letters too(y))
You need a equation with an isolated y, and you already have one, the initial one(y=-4x-7), and since x=-1:
<=>y=-4(-1)-7(always solve multiplications or divisons first, only then + or -)
<=>y=4-7<=>y=-3

Soluction (x=-1; y=-3)

Answer 4

subsitute the -4x-7 in for y in the first equation. 4x-2(-4x-7)=2
Multiply the stuff out... 4x+8x+14=2. combine like terms by bringing your 14 to the other side of the equal sign. 12x=2-14.
Combine again, 12x=-12. Divide the 12 off the x. so you get x=-12/12 which obviously equals -1. So x=-1. Take the -1 and substitute that in for your x in your second equation. y=-4(-1)-7.
Multiply and combine... y=4-7... y=-3. Your solution is (-1, -3).

Answer 5

I guess you know that when you want to transfer some of the members of the equation to the other side of the = side, they switch their sign.

4x-2y=2 =>
4x = 2y + 2 =>
2y = 4x - 2 /:2 (divide everything by 2) =>
y = 2x - 1

and you also have that y = -4x -7.

So, from both equations, you can write:
2x-1 = -4x - 7 =>

2x + 4x = -7 + 1

6x = -6 /:6 (divide everything by 6)

x = -1

Hope this was step by step enough for you :)

Answer 6

Assuming u r solving for X:

1) 4x-2y=2

4x=2y+2 (added 2y to both sides)

x=(y+1)/2 (divided both side by 4)

2) y=4x-7

4x-7=y (just flip the equation to see it in the x 1st order)

4x=y+7 (add 7 to both sides)

x=(y+7)/4 (divided both sides by 4)

Answer 7

If you are asking about simultaneous equations you would do it like this...
substitute y = -4x - 7 into the other equation:
4x - 2(-4x - 7) = 2
This gives:
4x + 8x + 14 = 2
Simplifies to:
12x = -12
Therefore divide by 12 and it gives:
x = -1
We can now use this value in the equation...y = -4(-1) - 7
This gives:
y = -3
Hope that helps!

Answer 8

substitut for y

4x- 2*(-4x-7) = 2
4x - (-8x -14) = 2
4x + 8x +14 = 2
12x = -12
x=-1

4*(-1) - 2y=2
-4 - 2y =2
-2y = 6
y= -3

Answer 9

2x+y+z=5 ..........a million 3x+y+6z=7 ............2 2x+9y+4z=13 .........3 employing d value of z from a million in 2 and 3 3x+y +30-12x-6y=7 or 9x+5y =23 ......(4) additionally 2x+9y +20 -8x-4y =13 6x -5y =7 ......(5) including 4 and 5 x =2 , employing this in 4 y = a million and z=0

Answer 10

4x-2y=2
4x+y=-7
subtracting
-3y=9
y=-3
substituting
4x+6=2
4x=-4
x=-1
soln.set{-1,-3}