algebra homework help pleeeeaaaasssseeee???????

Question

ive been working on this question for almost an hour now, and just cant get it, here it is:
3x-y=1 and 2x-5y=18 solve for x and y
showing me your work would be very helpful too

Answer 1

Remember that in algebra you can rearrange things by doing the same thing to both sides. Since both sides of the equal sign are different expressions of the same thing, you can add or subtract one equation to/from the other:

3x - y = 1
2x -5y =18

If I subtract the bottom equation from the top one, it actually won't help me yet because I need to do one more rearrangement before taking that step:

Try multiplying both sides of the top equation by 5:

5(3x - y) = 5 (1)

and you get:

15x - 5y = 5

Now you have -5y in both equations and you can do subtract the equations from each other like this:

15x - 5y = 5
- 2x - 5y =18
___________
13x - 0 = -13

or 13x = -13

Divide both sides by 13 to get x all by itself:

13x /13 = -13 / 13

and you get:

x = -1

Now plug -1 for x in one of the equations and then solve for y:

3 (-1) -y = 1 Simplify --> -3 -y = 1
Get the variable (y) by itself on one side of the equal sign by subtracting -3 from both sides: -3 - (-3) -y = 1 - (-3)
and you get: -y = 4
Multiply (or divide) both sides by -1 and you get y = -4

Test for y = -4 and x = -1 on both equations:

3(-1) - (-4) = 1 2(-1) - 5(-4) = 18
(-3) - (-4) = 1 (-2) - (-20) = 18
True: This does = 1 True: This does = 18

Thus, when x = -1 and y = -4 both equations are true, so x = -1 and y = -4.

Hope this helps!
-Rodney

Answer 2

Erin, its eeeeeeeezzzeeeeee.
Call 3x - y = 1 equation A
Call 2x -5y = 18 equation B.

Now if you could multiply one equation or the other by something so that the coeffiicent of x or y would equal the NEGATIVE of the coefficient of x or y in the other equation, what would be an easy choice.

Being lazy, if would multiply equation A by -5 . This gives me -15x +5 y= -5. Now I ADD the two equations, to get equation C:
-13 x = 13 equation C, from which x=-1.
Now you can substitute this in either equation A or B to get y.

Sometimes, you can't be all that lazy, so you have to multiply one equation by a factor and the other equation by another factor so that the resulting coefficients will add or subtract out to zero, but lets save that for another day.

Answer 3

Ok. The easiest way to solve this problem is the substitution method. I'd suggest taking the first equation and manipulating it as follows.

3x - y = 1
-y = -3x + 1
y = 3x - 1

Now, substitute for y in the second equation and solve for x.

2x - 5y = 18
2x - 5(3x - 1) = 18
2x - 15x + 5 = 18
-13x = 13
x = -1

Then, solving for y using the first equation provides the total answer.

y = 3x -1 = 3(-1) - 1 = -3 - 1 = -4.

Answer 4

This problem can be solved by either of two methods. You can solve both equations together or you can re-arrange one equation to solve for one variable in terms of the other variable and then substitute that solution into the other equation. Put another way, solve the first equation for y in terms of x and then substitute your answer into the second equation. Given that you are asking for work to be shown, the less sophisticated method may be more helpful and meaningful to you in learning what has apparently been skipped in class. That method is much longer, but it is more explanatory.

3x - y = 1 (first equation)
-y = 1 - 3x (isolating the y variable on one side of the equation, by adding a negative 3x to both sides)
y = 3x - 1 (multiplying both sides by -1 and re-arranging order of terms)

2x - 5y = 18 (second equation)
2x - 5(3x - 1) = 18 (substituting (3x -1 ) for y in second equation, since first equation says that y = (3x -1)
2x - 15x + 5 = 18 (removing parentheses with attention to negative sign of the multiplier (-5))
-13x + 5 = 18 (combining like terms)
-13x = 13 (isolating the x variable on one side of the equation)
13x = -13 (multiplying both sides of equation by negative 1)
x = -1 (solving for x by dividing both sides of equation by 13)

Solving for y (if x = -1)
first equation says that y = (3x -1)
y = 3(-1) - 1 (substituting)
y = -3 - 1
y = -4

Demonstrating Proof:
2x - 5y = 18
2(-1) - 5(-4) = 18 (substituting values for x and y)
-2 +20 = 18 (removing parentheses with attention to negative sign of multiplier (-5))
18 = 18 (combining terms)
Thus you have proven that x = -1 and y = -4

Answer 5

3x-y=1 and 2x-5y=18
since the coefficient of y in the first problem is -1(or 1) it will be easiest to solve for
3x-y=1
-y = 1- 3x
y = 3x - 1
Now we'll substitute for the y in the 2nd equation
2x-5y = 18
2x-5(3x-1) = 18
Distribute and simplify
2x - 15x+5
-13x + 5 = 18
-13x = 13
x = -1
Now to solve for y sub into either equation
3 x - y = 1
3(-1) - y = 1
-3 - y = 1
-y = 4
y = -4
(x,y)=(-1,-4)

Answer 6

Ok. Take this:

3x-y = 1 -> (-5)(3x-y=1)-> -15x + 5y = -5
2x-5y=18 ->2x-5y=18 -> (+) 2x - 5y = 18
Then you get -13x = 13, so x = -1

Then substitute the x into one of two problems, like so :
3(-1) - y = 1; -3 -y = 1; -y = 4; y = -4

(x, y) = (-1, -4)

Answer 7

3x - y = 1 -> 15x - 5y = 5 -> -15x + 5y = -5 using that 2x - 5y = 18 and adding them we will get that (-13)*x = 13. This means that x = -1 and y = -4.

Answer 8

Okay.. you can use substitution.. It's easier in this problem. If you subtract 3x and times every term by -1, you will get y=3x-1 right? then you substitute that into the second equation. it will be 2x- 5(3x-1)= 18. Then it will be -13x+5=18. you subtract 5 from both sides. you will get -13x=13, x= -1. You plug in that to the first equation and get y= -4. if you dont get it.. feel free to email me at [e-mail]

Answer 9

I used a program on the internet to do Cramer's rule.

x=-1
y=-4

Checks
3(-1)-(-4)
-3+4=1
1=1

2(-1)-5(-4)
-2+20=18
18=18

Answer 10

OK what you have to do is get X and Y alone. However you can only do this with one at a time. What you do is this:
3x-y=1 -> y= -3x+1 -> y= -3(0)+1 -> y=1

What you have to do is make the variables =0 one at a time. You will get the answer but make sure you get the variables alone first.