Solve these linear equations please? goodluck...?

Question

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


4x + 3y/2 = -8

Answer 1

Take LCM in EQUA.1

(4x-3y)/6=1/6
4x-3y=1/6 x 6
4x-3y=1.......................................................P
4x+3y/2=-8
Take LCM
(8x+3y)/2=-8
8x+3y=-8 x 2
8x+3y=-16.....................................................S
4x-3y=1
8x+3y=-16
multiply 8 in P and 4 in S
4x-3y=1 x 8
8x+3y=-16 x4
______________
32x-24y=8
32x+12y=-64
- - +
_______________
-36y=72
multiply by '-' on both sides
-(-36y)=-72
+36y=-72
y=-72/36
y=-2
substitue y=-2 in EQUA P
32x-24(-2)=8
32x+48=8
32x=-40
x=-40/32
x=-5/4
Verification:-
2(-5/4)/3 - (-2)/2=1/6
-10/4/3/1+2/2=1/6
-10/12+1=1/6
-5/6+1/1=1/6
-5+6/6=1/6
1/6=1/6
LHS=RHS
(x,y)=(-5/4,-2)

Answer 2

The equation for a line is y=mx+b. m is the slope; b is the y-intercept, i.e where it hits the y-axis. The first question starts by asking for a line with slope -4. So you know your equation will be y=-4x+b. What's b? Now we plug in our point, (2,-3). -3=-4*2+b. -->b=5. We can pull the same trick on the next one. y=mx+b. Our point is (-4, -5), and our slope (m) is 3/2. So we plug it in; -5=(3/2)(-4)+b.--> -5=-6+b-->6-5=b-->b=1. So the answer is y=(3/2)x+1. For the next one we get that the slope is zero, so our equation will be y=(0)x+b. That means it must be y=4.6. The next few problems give you two points, and no slope. However we can find the slope! It's just "rise over run", or (y_1-y_2)/(x_1-x_2). Pick one of the points to be (x_1,y_1) and the other to be (x_2,y_2). then you can find m, and proceed as before. E.g. for problem 15, m=(7-5)/(5-2)=(2)/(3)=(2/3). Then you can plug in points again: 5=(2/3)*2+b-->5=(4/3)+b-->b=5-(4/3)=(15/... Putting that together, we have y=2/3x+11/3. The next few questions are similar. Then we get a few about slope. To find the slope, write the equation as y=mx+b, then get the m. For example, the first one, 4x+y=3, can be written y= -4x+3, so the slope is -4. If there is no x, like in question 21, your slope is 0. (Think of it as y=(0*x+2). Sometimes you'll run across an equation that has no y, like q.22. In this case (draw it on a graph!) you'll notice the line is vertical. That means the slope is undefined. If you picked two points on it--(4,0) and (4,1), say--and tried to find the slope between them, you'd find it was (1-0)/(4-4)=1/0 which is undefined. Finally we have a few that ask about parallel lines. Keep in mind that parallel is code for "has the same slope as". So, first look at the slope of the equation they give you. Then, you can rephrase the question to be like the first ones--"What is the line with this slope that goes through this point?" and solve.

Answer 3

I am assuming you want to find the slope intercept form of the equation.y = mX + b

4x + 3y/2 = -8

3y/2 = -8 -4x
minus 4x on both sides to isolate y

3y = 2 (-8 - 4x)
multiply both sides by 2 to get rid of the fraction to get 3y = -16 - 8x

y = (-16 - 8x)/3

Divide by 3 to get y alone

y = -8/3 (x) - 16/3

I hope that was the question you were asking and not solving the two equations simultaneously (which is different).

Answer 4

rearrange the second equation,
x = -(2 + 3y/8)

now substitute x into the first equation and solve for y,
-2(2 + 3y/8) - y/2 = 1/6
-4 - 3y/4 - y/2 = 1/6
-5y/4 = 25/6
-15y/12 = 50/12
-15y = 50
y = -50/15
y = -10/3

now substitute y back into any equation and solve for x
(i pick the second one)

4x + 3(-10/3)/2 = -8
4x - 5 = -8
4x = -3
x = -3/4

Answer 5

4x - 3y = 1
y = 4/3x - 1/3
you will have to find two points and draw the line
if x = 0 y = -1/3 so A(0, -1/3) is one point
and if x = 1 y=1 so B(1,1)
the solution is the line (that you have to draw) passing thru points A and B


8x + 3y = -16
y = -8/3x -16/3
If x = 0 y = -16/3 A(0,-16/3)
if x = 1 y = -8 B(1, -8)
the solution is the line passing thru points A & B

Answer 6

2x/3 - y/2 = 1/6 -------------(1)
4x +3y/2 = -8 ---------------(2)
(1)*3 we get,
2x - 3y/2 = 1/2
4x +3y/2 = -8
adding these two equations we get,
6x = -15/2 ,so, x = -5/4
substituting this value of x in equation (1) we get the value of y as -2.

Answer 7

2x/3 - y/2 = 1/6 multiply by 3
2x-3/2y=1/2
4x + 3y/2 = -8 add
6x=-7.5 divide by 6
x=1.25=5/4
4x + 3y/2 = -8 substitute x=5/4
4(5/4)+3y/2=-8
5+3y/2=-8 subtract 5 from each side
3y/2=-13 multiply both sides by 2/3
y=-26/3
(5/4, -26/3)

Answer 8

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

Multiplying by the LCM of 3, 2, and 6 (which is 6) to both sides, to get

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

4x - 3y = 1

In slope-intercept form,

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

Do the other one yourself using the same method.

Answer 9

Do your own homework.

Answer 10

hey EINSTEIN!

i cant answer it

im sick of math!!