Algebra Points: Give the solution set to the system: 3x + 2y = 3 and 63x – 36y = 11.?

Question

Note: The answer contain fraction bars with parenthesis e.g. {(#,#)} or {(#/#,#/#)}.

Best answer will be selected tommorrow!

Answer 1

1. Multiply both sides of the first equation by 21: 63x + 42y = 63
2. Subtract the 2nd eq. from the 1st: 78y = 52
3. Divide both sides by 78: y = 52/78 = 2/3
4. Substitute 2/3 for y in the first equation: 3x + 2(2/3) = 3
5. Simplify 2(2/3): 3x + 4/3 = 3
6. Subtract 4/3 from both sides: 3x = 3 - 4/3 = 9/3 - 4/3 = 5/3
7. Divide both sides by 3: x = 5/9

So the answer is (5/9, 2/3).

Answer 2

You can solve this equation many ways, but the best way to solve this problem (in my opinion) would be by using the elimination process since you may want to avoid having to deal with fractions during your journey to the answer. (Haha, that sounded so magical .. "journey")

Let's start off by seeing what we have right now:
3x+2y=3
63x-36y=11

We can eliminate x or y.

By eliminating x, we will want it to have the same coefficient values with one being the negative.
3x+2y=3
63x-36y=11
The coefficients for x are 3 and 63. Obviously, the common multiple of these two numbers is 63. Since the second equation has a positive coefficient, we will want the first equation to have a negative coefficient, thus canceling it out.
Multiply -21 to the first equation:
-21(3x+2y=3)
-63x-42y=-63
Now take the second equation and add it to your first.
-63x-42y=-63
63x-36y=11
------------------
0x-78y=-52
-78y=-52
Now that you have only one variable in the equation, solve for it:
(-78y/-78)=(-52/-78)
y=52/78
Simplified: y=2/3
Taking the y value and plugging it back in to your original equation will give you the value of x:
63x-36y=11
63x-36(2/3)=11
63x-24=11
63x=35
x=35/63
Simplifed: x=5/9

Your answer will be in the ordered pair (x,y): (5/9, 2/3)
Since it is a solution set, you would write it like this:
{(5/9, 2/3)}

ALWAYS CHECK YOUR WORK:
3x+2y=3
3(5/9)+2(2/3)=3 ?
(5/3)+(4/3)=3 ?
(9/3)=3 ?
3=3 Check.
Just because it checks for one equation does not mean it is correct. Check the second equation as well (I am a paranoid child in math class.)
So let's check the other equation as well:
63x-36y=11
63(5/9)-36(2/3)=11 ?
35-24=11 ?
11=11 Check.

The answer is correct! (*sighs in relief*)
3x+2y=3
63x-36y=11
Solution set: {(5/9, 2/3)}

Of course, you could have done this by eliminating y instead of x at the beginning. You will get the same answer. Try it out! :]

Answer 3

The answer I have are (-7.33, 12.33). I don't know these answers in fraction form. What I did was I multipied the whole equation 3x+2y=3 by -21 and got -63x+42y=63. Then I adding this equation to the second equation to cancelled out the Xs. Then I solved for y and got the y value. Then I plugged in the Y value into the equation 3x+2y=3 and solved for x. That is how I got the answer. I hope it is right and I hope I have helped you. To check to see if it is right just plugged in the anwers into the orginal problems. The answers might be a little off because I rounded but it should be close.

Answer 4

Solve by subsitution.

Rearrange first equation in terms of x

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

Substitute into other equation

63(1 - (2/3)y) - 36y = 11
63 - 42y - 36y = 11
52 = 78y
y = 2/3

Sub y value back into either equation

3x + 2(2/3) = 3
3x = 5/3
x = 5/9

Answer = {(5/9), (2/3)}

Answer 5

No more than solving a two equations system with two variables:

3x+2y=3 (1)
63x-36y=11 (2)

from (1):

x=(3-2y)/3 and replacing this expresion for this variable on (2):

63(3-2y)/3-36y=11 then placing y on the left:

63-42y-36y=11
-78y=11-63
y=52/78=0.66 and then replacing this value on (1):

3x+2*0.66=3, finally this gives:
x=(3-1.32)/3=0.56

then the answer will be (0.56, 0.66) having in mind that this values has only two decimal precision

Answer 6

3x + 2y = 3
63x - 36y = 11

3x + 2y = 3
2y = -3x + 3
y = (-3/2)x + (3/2)

63x - 36y = 11
63x - 36((-3/2)x + (3/2)) = 11
63x + (108/2)x - (108/2) = 11
63x + 54x - 54 = 11
117x - 54 = 11
117x = 65
x = (65/117)
x = (5/9)

y = (-3/2)x + (3/2)
y = (-3/2)(5/9) + (3/2)
y = (-15/18) + (3/2)
y = (-5/6) + (3/2)
y = (-5/6) + (9/6)
y = (-5 + 9)/6
y = (4/6)
y = (2/3)

ANS : ((5/9),(2/3))

Answer 7

Multiply the first equation by 18 and and the two equations. Solve for x. Then replace x to any equation and solve for y. The answer is:
(5/9, 2/3)

Answer 8

3x + 2y = 3 (x18)
54x+36y = 54
36y = 54 - 54x

63x - 36y = 11
63x - (54 - 54x) = 11
117x - 54 = 11
117x = 65
x = 65/117

Answer 9

Don't you just use the substitution method or that subtraction method. Either way you just set them equal to each other. Do your own homework!

Answer 10

(.55555555555555555556, .66666666666666666667)

or (65/117, 78/117)