math problem?

Question

Solve each system of equations. If the system has no solution, say that it is inconsistent

{3x - 6y = 2
{5x + 4y = 1

Can you please help with this?

Answer 1

5(3x-6y)=2(5)
15x-30y=10

-3(5x+4y)=1(-3)
-15x-12y=-3

taking the results of the above:

15x-30y=10
-15x-12y=-3
__________ combine
0x-42y=7

divide by -42 on both sides
y= -1/6

substitute into 1st equation:

3x-6( -1/6)=2
3x+1=2
3x=1 after subtracting 1 from each side
divide by 3
x=1/3

now check by substituting into second derived equation:

15x-30y=10

15(1/3) -30( -1/6)=10

5+5=10
checks

Answer 2

Let's eliminate the y-terms. We have -6y in the first equation and +4y in the second, so if we take twice the first equation plus three times the second equation we will get a -12y and a +12y and they will cancel out.
So we get
2(3x) + 3(5x) + 2(-6y) + 3(4y) = 2(2) + 3(1) [you'd normally skip this step and just go to the next line:]
<=> 21x = 7
<=> x = 1/3
Then 3x - 6y = 2
<=> 1 - 6y = 2
<=> y = -1/6.
So the solution is x = 1/3, y = -1/6.

Answer 3

okay what i would first do is solve for y in one of the equations (probably 3x-6y=2 would be easiest). Which would be y= 1/2x-1/3.. then substitute 1/2x-1/3 into the 5x+4y=1 placing it in the variable y. Solve and there is your "y" then solve for x using y. Hope that helps

Answer 4

*Isolate "x" or "y" in either equation. let's isolate "y" in the 2nd equation.

First: subtract 5x from both sides (when you move a term to the opposite side, always use the opposite sign).

5x+4y = 1
5x-5x+4y = 1-5x
4y = 1-5x (divide each term by 4).
4y/4 = 1/4 - 5x/4
y = 1/4 - 5x/4

SEc: substitute "1/4 - 5x/4" with "y" in the 1st equation.

3x-6y = 2
3x - 6(1/4 - 5x/4) = 2
3x - 6(1/4)-6(-5x/4) = 2
3x - 6/4 - (-30x/4) = 2
3x - 6/4+30x/4 = 2
3x - 3/2+15x/2 = 2
3x+15x/2 - 3/2 = 2
21x/2 - 3/2 = 2 (add 3/2 to both sides).
21x/2 - 3/2+3/2 = 2 +3/2
21x/2 = 2+3/2
21x/2 = 7/2 (multiply the reciprocal of 21x/2 with both sides).
(2/21)(21x/2) = (2/21)(7/2)
x = (2/21)(7/2) = 14/42 > simplify = 1/3

Third: substitute 1/3 with "x" in the 2nd equation.

(2) 3x-6y = 2
3(1/3) - 6y = 2
3/3 - 6y = 2
1 - 6y = 2 (subtract 1 from both sides).
1-1-6y = 2-1
- 6y = 2-1
- 6y = 1 (divide both sides by -6).
-6y/-6 = 1/-6
y = 1/-6 = -1/6

Solution: (1/3, -1/6)

Answer 5

im not doing it for you but you have to cancel out either the y or the x

x multiply the top by all by -5 and the bottom all by 3
y multiply the top by 2 and the bottom by 3

Answer 6

You have to cancel one of the variables out and then plug the first variable in the second equation to determine the second variable.

Answer 7

r u supposed 2 graph dis ...or am i off topic cuz dat's how i did one of my hws

Answer 8

i hate math

Answer 9

Nope! I don't do other peoples homework. Please do your own homework. Cheating is against school rules you know!

Answer 10

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