以下の3つの連立方程式をそれぞれ解く。 (a) $y = -10x + 7000$ $y = 10x + 1000$ (b) $2000 = 100x + y$ $1500 = 100x + \frac{1}{2}y$ (c) $5y = x - 5$ $2x - 3y = 115$

1. 問題の内容

以下の3つの連立方程式をそれぞれ解く。

(a)

$y = -10x + 7000$

$y = 10x + 1000$

(b)

$2000 = 100x + y$

$1500 = 100x + \frac{1}{2}y$

(c)

$5y = x - 5$

$2x - 3y = 115$

2. 解き方の手順

(a)

$y$ の値を代入して、$x$ について解く。

$-10x + 7000 = 10x + 1000$

$20x = 6000$

$x = 300$

$x = 300$ を $y = 10x + 1000$ に代入して、$y$ を求める。

$y = 10(300) + 1000 = 3000 + 1000 = 4000$

(b)

$2000 = 100x + y$ より、$y = 2000 - 100x$

$1500 = 100x + \frac{1}{2}y$ に代入

$1500 = 100x + \frac{1}{2}(2000 - 100x)$

$1500 = 100x + 1000 - 50x$

$500 = 50x$

$x = 10$

$y = 2000 - 100x = 2000 - 100(10) = 2000 - 1000 = 1000$

(c)

$5y = x - 5$ より、$x = 5y + 5$

$2x - 3y = 115$ に代入

$2(5y + 5) - 3y = 115$

$10y + 10 - 3y = 115$

$7y = 105$

$y = 15$

$x = 5y + 5 = 5(15) + 5 = 75 + 5 = 80$

3. 最終的な答え

(a) $x = 300, y = 4000$

(b) $x = 10, y = 1000$

(c) $x = 80, y = 15$