Question

{-1,5x+2cos y =-5,5. {4x+10cos y=7

Answer 1

Відповідь:

To solve the given system of equations:

Equation 1: -1.5x + 2cos(y) = -5.5

Equation 2: 4x + 10cos(y) = 7

We can use the method of substitution to find the values of x and y. Firstly, let's solve Equation 1 for x:

-1.5x = -2cos(y) - 5.5

x = (2cos(y) + 5.5) / 1.5

Now, substitute this value of x into Equation 2:

4((2cos(y) + 5.5) / 1.5) + 10cos(y) = 7

Simplifying this equation will give us the value of y. Let's solve it step by step:

(8cos(y) + 22) / 1.5 + 10cos(y) = 7

(8cos(y) + 22 + 15cos(y)) / 1.5 = 7

(23cos(y) + 22) / 1.5 = 7

23cos(y) + 22 = 7 * 1.5

23cos(y) + 22 = 10.5

23cos(y) = 10.5 - 22

23cos(y) = -11.5

cos(y) = -11.5 / 23

cos(y) = -0.5

Now, we can find the value of y by taking the inverse cosine (arccos) of -0.5:

y = arccos(-0.5)

y ≈ 120° or 240° (since cos has a period of 360°)

Finally, substitute the value of y back into Equation 1 to find x:

x = (2cos(y) + 5.5) / 1.5

Substituting y = 120°:

x = (2cos(120°) + 5.5) / 1.5

x = (-1 + 5.5) / 1.5

x ≈ 2

Substituting y = 240°:

x = (2cos(240°) + 5.5) / 1.5

x = (-1 + 5.5) / 1.5

x ≈ 2

Therefore, the solution to the given system of equations is:

x ≈ 2 and y ≈ 120° or 240°.