(16) $$ \left\{\begin{array}{l}3 x-2(y+2)=28 \ \frac{x}{3}+\frac{y}{7}=1\end{array} ight. $$

Question

(16) $$ \left\{\begin{array}{l}3 x-2(y+2)=28 \ \frac{x}{3}+\frac{y}{7}=1\end{array}ight. $$

UpStudy AI · Accepted Answer

Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}3x-2\left(y+2\right)=28\\frac{x}{3}+\frac{y}{7}=1\end{array}\right.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=\frac{32+2y}{3}\\frac{x}{3}+\frac{y}{7}=1\end{array}\right.$$
- step2: Substitute the value of $$x:$$
  $$\frac{\frac{32+2y}{3}}{3}+\frac{y}{7}=1$$
- step3: Divide the terms:
  $$\frac{32+2y}{9}+\frac{y}{7}=1$$
- step4: Multiply both sides of the equation by LCD:
  $$\left(\frac{32+2y}{9}+\frac{y}{7}\right)\times 63=1\times 63$$
- step5: Simplify the equation:
  $$224+23y=63$$
- step6: Move the constant to the right side:
  $$23y=63-224$$
- step7: Subtract the numbers:
  $$23y=-161$$
- step8: Divide both sides:
  $$\frac{23y}{23}=\frac{-161}{23}$$
- step9: Divide the numbers:
  $$y=-7$$
- step10: Substitute the value of $$y:$$
  $$x=\frac{32+2\left(-7\right)}{3}$$
- step11: Calculate:
  $$x=6$$
- step12: Calculate:
  $$\left\{ \begin{array}{l}x=6\y=-7\end{array}\right.$$
- step13: Check the solution:
  $$\left\{ \begin{array}{l}x=6\y=-7\end{array}\right.$$
- step14: Rewrite:
  $$\left(x,y\right) = \left(6,-7\right)$$
与えられた連立方程式は次の通りです：

1. $$ 3x - 2(y + 2) = 28 $$
2. $$ \frac{x}{3} + \frac{y}{7} = 1 $$

この方程式を解くと、解は次のようになります：

$$
(x, y) = (6, -7)
$$

したがって、$$ x = 6 $$ および $$ y = -7 $$ です。
$$ x = 6 $$ および $$ y = -7 $$

(16)

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