Question

6y-5x=1 x-1/2+3y-x/4=-4 3/4​

Answer 1

Ответ:(x,y)=(-15/26,-397/312)

Answer 2

To solve the system of equations:

1. 6y - 5x = 1
2. x - 1/2 + 3y - x/4 = -4 3/4

We can use the method of substitution or elimination. Let's use the elimination method to solve this system of equations.

First, let's rewrite the second equation to make it easier to work with:

2. -1/2 + 3y - x/4 = -4 3/4

Now, we can eliminate one of the variables by adding or subtracting the equations to cancel out one variable. Let's eliminate x. To do that, we'll multiply both sides of the first equation by 4 and the second equation by 20 to make the coefficients of x in both equations equal:

1. Multiply the first equation by 4: 4(6y - 5x) = 4(1) 24y - 20x = 4

2. Multiply the second equation by 20: 20(-1/2 + 3y - x/4) = 20(-4 3/4) -10 + 60y - 5x = -95

Now, we have:

3. 24y - 20x = 4
4. -10 + 60y - 5x = -95

We can subtract equation 4 from equation 3 to eliminate x:

(24y - 20x) - (-10 + 60y - 5x) = (4 - (-95))

Simplify:

24y - 20x + 10 - 60y + 5x = 99

Combine like terms:

-36y + 10 = 99

Now, isolate y by moving 10 to the other side:

-36y = 99 - 10 -36y = 89

Divide by -36 to solve for y:

y = 89 / -36 y = -89/36

Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x. Let's use equation 1:

6y - 5x = 1 6(-89/36) - 5x = 1

Now, simplify and solve for x:

-534/36 - 5x = 1

-267/18 - 5x = 1

To clear the fraction, you can multiply both sides by 18:

-267 - 90x = 18

Now, isolate x:

-90x = 18 + 267 -90x = 285

Divide by -90 to solve for x:

x = -285 / -90 x = 19/6

So, the solution to the system of equations is:

x = 19/6 y = -89/36