What is the solution of the system of linear equations 3y equals 3 over 2x + 6/2 y - 1/4 x equals 3

(x, y) = (8, 5)

Step-by-step explanation:

I like to use a graphing calculator with weird equations like these. (See the attached.)

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If you want to solve by hand, you can eliminate fractions, then use your favorite method: substitution, elimination, Cramer's rule, graphing, matrix methods, guess and check, whatever.

Multiply the first equation by 2.

... 6y = 3x +6

This has a factor of 3 that can be removed, and it can be put into standard form by subtracting y and the constant.

... x - 2y = -2

Multiply the second equation by 4.

... 4y - x = 12

You can add these equation to eliminate x.

... (x -2y) +(4y -x) = (-2) +(12)

... 2y = 10 . . . . . . simplify

... y = 5 . . . . . . . . divide by the coefficient of y

Now you can use either equation to find x.

... x - 2·5 = -2

... x = 10 -2 = 8

Then the solution is (x, y) = (8, 5).

0 is its x and y coordinate

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)