Question

Решите уравнения x2+7xy+y2=9 3x-2y=1

Answer 1

  x2+7xy+y2=9 . Пусть y=1, x2+7x+2=9,  x=7/9. 
 
  3x-2y=1 Пусть  y=1, тогда 3x-2=1, x=1

Answer 2

To solve the system of equations, we can use either the substitution method or the elimination method. Let's use the elimination method:

Given equations:

1. $x^2 + 7xy + y^2 = 9$ ............(i)
2. $3x - 2y = 1$ ...............(ii)

Step 1: Solve equation (ii) for $x$ or $y$. $3x - 2y = 1$ => $3x = 2y + 1$ => $x = \frac{2y + 1}{3}$

Step 2: Substitute the value of $x$ into equation (i): $\left(\frac{2y + 1}{3}\right)^2 + 7\left(\frac{2y + 1}{3}\right)y + y^2 = 9$

Step 3: Simplify and solve for $y$: $\frac{4y^2 + 4y + 1}{9} + \frac{14y^2 + 7y}{3} + y^2 = 9$

Multiply everything by 9 to eliminate fractions: $4y^2 + 4y + 1 + 14y^2 + 7y + 9y^2 = 81$

Combine like terms: $27y^2 + 11y + 1 = 81$

Step 4: Rearrange the equation and set it to zero: $27y^2 + 11y + 1 - 81 = 0$

Step 5: Solve the quadratic equation for $y$. We can factor it or use the quadratic formula:

Using the quadratic formula: $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a = 27$, $b = 11$, and $c = -80$.

$y = \frac{-11 \pm \sqrt{11^2 - 4 \cdot 27 \cdot (-80)}}{2 \cdot 27}$

$y = \frac{-11 \pm \sqrt{121 + 8640}}{54}$

$y = \frac{-11 \pm \sqrt{8761}}{54}$

The solutions for $y$ will be the two possible values.

Step 6: Once you have the values for $y$, you can find the corresponding values for $x$ using equation (ii): $x = \frac{2y + 1}{3}$

After obtaining the numerical values for $x$ and $y$, you should have two sets of solutions for $x$ and $y$.