Question

解二元一次方程组3(x+y)-4(x-y)=4 x+y/2+x-y/6=1

Answer 1

解:3(x
+
y)
-
4(x
-
y)
=
4
①
x
+
y/2
+
x
-
y/6
=
1
②
由①得
7y
-
x
=
4
③
由②得
2x
+
y/2
-
y/6
=
1
2x
+
3y/6
-
y/6
=
1
2x
-
y/6
=
1
12x
-
y
=
6
④
③
+
④
×
7得
83x
=
46
x
=
46/83
把
x
=
46/83代入
③得
7y
-
46/83
=
4
7y
=
4
+
46/83
7y
=
378/83
y
=
378/581
∴
原方程组的解为
x
=
46/83
y
=
378/581
如果原方程是“3(x
+
y)
-
4(x
-
y)
=
4
x
+
y)/2
+
(x
-
y)/6
=
1
”的话，可以作如下解答。
解:
3(x
+
y)
-
4(x
-
y)
=
4
①
(x
+
y)/2
+
(x
-
y)/6
=
1
②
②
×
6得
3(x
+
y)
+
(x
-
y)
=
6
③
③
-
①得
5(x
-
y)
=
2
x
-
y
=
2/5
④
把x
-
y
=
2/5代入①得
3(x
+
y)
-
4
×
2/5
=
4
3(x
+
y)
=
48/5
x
+
y
=
16/5
⑤
④
+
⑤得
2x
=
18/5
x
=
9/5
把x
=
9/5代入
④得
9/5
-
y
=
2/5
y
=
9/5
-
2/5
y
=
7/5
∴
原方程组的解为
x
=
9/5
y
=
7/5