Question

Решите систему уравнений

Answer 1

1/x=a,1/y=b
{2a+b=4/*3⇒6a+3b=12
{a-3b=9
прибавим
7a=21
a=21:7
a=3⇒1/x=3⇒x=1/3
6+b=4
b=4-6
b=-2⇒1/y=-2⇒y=-1/2
(1/3;-1/2)

Answer 2

Solving the System of Equations

To solve the system of equations, we will use the information provided in the search results. Let's examine the available snippets to find a suitable system of equations to solve.

From the snippets, we have the following options:

1. Snippet 2x-y=7, x^2-xy=12 2. Snippet 3x-y=3, 3x-2y=0 3. Snippet 2ab - 3a/b = 15, ab + a/b = 10 4. Snippet y=x-8, xy=-7 5. Snippet 10-8-20=6-13, 4-63=20-10+2

Let's choose the first option, Snippet which provides the system of equations 2x-y=7 and x^2-xy=12.

To solve this system, we can use substitution or elimination methods. Let's use the substitution method:

1. Solve the first equation for y: y = 2x - 7. 2. Substitute this expression for y in the second equation: x^2 - x(2x - 7) = 12. 3. Simplify and solve for x: x^2 - 2x^2 + 7x - 12 = 0. 4. Combine like terms: -x^2 + 7x - 12 = 0. 5. Factor the quadratic equation: -(x - 3)(x - 4) = 0. 6. Set each factor equal to zero and solve for x: - x - 3 = 0, so x = 3. - x - 4 = 0, so x = 4.

Now that we have the values of x, we can substitute them back into the first equation to find the corresponding values of y:

For x = 3: - 2(3) - y = 7 - 6 - y = 7 - y = -1

For x = 4: - 2(4) - y = 7 - 8 - y = 7 - y = 1

Therefore, the solution to the system of equations 2x-y=7 and x^2-xy=12 is (x, y) = (3, -1) and (4, 1).

Please let me know if there's anything else I can help you with!