Question

6x-4y=8 -6x+10y=13 mmmmmmmmmmmmmm

Answer 1

Ответ:

6х-4у-6х+10у=13+8

6у=21

у=21/6=7/2=3.5

6х-4*(3.5)=6х-14=8

6х=22

х=22/6=11/3

Объяснение:

Answer 2

To solve the system of equations:

6x - 4y = 8 ...(Equation 1) -6x + 10y = 13 ...(Equation 2)

We can use the method of elimination or substitution. Let's use the method of elimination:

To eliminate the x-term, we'll multiply Equation 1 by 1 and Equation 2 by 1.5 (to make the coefficients of x in both equations equal and opposite):

1*(6x - 4y) = 1*(8) 1.5*(-6x + 10y) = 1.5*(13)

Simplifying the equations, we get:

6x - 4y = 8 ...(Equation 1) -9x + 15y = 19.5 ...(Equation 2)

Now, we can add both equations to eliminate the x-term:

(6x - 4y) + (-9x + 15y) = 8 + 19.5

Simplifying the equation further:

-3x + 11y = 27.5 ...(Equation 3)

Now we have a new equation (Equation 3) in terms of only y and x. Let's solve Equations 3 and 2 simultaneously:

-3x + 11y = 27.5 ...(Equation 3) -6x + 10y = 13 ...(Equation 2)

To eliminate the y-term, we'll multiply Equation 3 by 10 and Equation 2 by 11:

10*(-3x + 11y) = 10*(27.5) 11*(-6x + 10y) = 11*(13)

Simplifying the equations, we get:

-30x + 110y = 275 ...(Equation 4) -66x + 110y = 143 ...(Equation 5)

Subtracting Equation 4 from Equation 5 to eliminate the y-term:

(-66x + 110y) - (-30x + 110y) = 143 - 275

Simplifying the equation further:

-36x = -132

Dividing both sides of the equation by -36, we get:

x = (-132)/(-36) = 11/3 = 3.67 (rounded to two decimal places)

Now that we have the value of x, we can substitute it back into either Equation 3 or Equation 2 to solve for y. Let's use Equation 3:

-3x + 11y = 27.5

Substituting x = 3.67:

-3(3.67) + 11y = 27.5 -11.01 + 11y = 27.5 11y = 27.5 + 11.01 11y = 38.51 y = 38.51/11 y = 3.50 (rounded to two decimal places)

Therefore, the solution to the system of equations is x ≈ 3.67 and y ≈ 3.50.