Tell me how you got these answers??! Algebra help?!?!?

Question

1. y=x-2
y=4x+1

2. 2x+3y=0
x+2y=-1

3. 1/2x+1/3y=5
1/4x+y=10

Dont tell me the answers plz, just tell me the steps and make it easy! Im studying for a huge midterm tomorrow =)

Answer 1

PROBLEM 1:

These are both already in terms of y, so it is easiest if you just equate them:

x - 2 = 4x + 1

Now solve as usual (subtract x from both sides):
-2 = 3x + 1

Subtract 1 from both sides:
-3 = 3x

Divide both sides by 3:
-3/3 = x
-1 = x

x = -1

Now plug that back into one of the original equations to get y:
y = -x - 2
y = (-1) - 2
y = -3

Answer (-1, -3)

PROBLEM 2:

Again, if you write the equations in terms of y, you can equate them:

Eq. 1:
2x + 3y = 0
3y = -2x
y = -(2/3)x

Eq. 2:
x + 2y = -1
2y = -x - 1
y = (- x - 1) / 2
y = -(1/2)x - (1/2)

Equate these:
-(2/3)x = -(1/2)x - (1/2)

I'd start by multiplying by -1 to get rid of the negative signs:
(2/3)x = (1/2)x + (1/2)

I'd also multiply by 6 (lowest common denominator) to get rid of fractions:
4x = 3x + 3

Now you can solve easily:
x = 3

Plug this back into one of your revised equations:
y = -(2/3)x
y = -(2/3)(3)
y = -2

Answer (3, -2)

PROBLEM 3:

Same method as #2.

Answer 2

1) since they both equal y just set them equal to eachother
x-2=4x+1
x=4x+3 y=4x+1
-3x=3 y=4(-1)+1
x=-1 y=-3
2)2x+3y=0 x+2y=-1 =>move the 2y over to get x=-2y-1 and plug that into the other equation
2(-2y-1)+3y=0 x=-2y-1
-4y-2+3y=0 x=-2(-2)-1
-y-2=0 x=3
-y+2
y=-2
3)this one i would multiply the second equation by two and subtract them so you get
[1/2x+1/3y=5]
-[1/2x+6/3y=20]

-5/3y=-15 1/2x+1/3y=5
-5y=-45 1/2x=5-1/3(9)
y=9 1/2x=2 x=1

Answer 3

for the first one since they both say y = , just set them equal to each other

x-2 = 4x + 1
-3 = 3x
-1 = x

y = -1 - 2
y = -3

2.
x = -2y - 1

2(-2y -1) + 3y = 0
-4y -2 + 3y = 0
-y = 2
y = -2

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

3.
I would get rid of the fractions

3x + 2y = 30
x + 4y = 40

x = -4y + 40

3(-4y + 10) + 2y = 30
-12y + 30 + 2y = 30
-10y = 0
y = 0

x = -4(0) + 40
x = 40

Answer 4

2(x-9) = -24 [Given] 2x - 18 = -24 [the two is dispensed to the x and 9, considering they are in parentheses] 2x - 18 = -24 + 18 + 18 [you should upload 18 so as that it eliminates the -18. The x must be via itself to resolve. you should upload 18 to the appropriate facet additionally, to make the equation balanced] 2x = -6 [After including 18 to the two sides, the appropriate facet equals -6 2x ÷ 2 = -6 ÷ 2 [back, you should get x via itself. So, divide the 2x via 2, and an identical with the different facet.] x = -3 [answer]

Answer 5

1)

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

y = 4x + 1 ----------eqn(2)

both LHS are equal to y so both RHS should be equal

x - 2 = 4x + 1

subtract x

-2 = 3x + 1

subtract 1

-2 - 1 = 3x

3x = -3, solve for x , then plug in x value in eqn(1) to get y value.

2)

2x + 3y = 0 -------------eqn(1)

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

multiply eqn(2) with 2 to equalise x terms in both the equations

2x + 4y = -2 ---------eqn(3)

subtract eqn(1) from (3)

solve for y , then plug in y value in eqn(1) or (2) and solve for x

3)

1/2 x + 1/3y = 5 ----------eqn(1)

1/4x + y = 10 --------------eqn(2)

multiply eqn(1) with 6 to get rid of fractions

3x + 2y = 30 --------eqn(3)

multiply eqn(2) with 12 to get rid of fraction and equilize x terms

3x + 12y = 120 ---------eqn(4)

subtract (3) from (4)

10y = 90

solve for y , then substitute y value in eqn(3) to get x value

Answer 6

you solve for x in one of the equations, for example:
y=x-2 (add 2 to both sides)
y+2=x
then substitute y+2 for x in the other equation.
y=4(y+2)+1
then you solve for y
y=4y+9
-3y=9
y=-3
then substitute y back into one of the original equations to fin the value of x

Answer 7

I know it hard cuz i am doing that to.Try u r best and think of a way u could work it out.Good luck!