【中学2年数学】2-1 連立方程式の解き方｜問題集
1.次の連立方程式を解きなさい。
(1)\(\left\{\begin{array}{l}x-5y=-2 \\ -x+2y=-1\end{array}\right.\)
\(\left\{\begin{array}{l}x=3 \\ y=1\end{array}\right.\)
(2)\(\left\{\begin{array}{l}2x-y=1 \\ 3x-y=5\end{array}\right.\)
\(\left\{\begin{array}{l}x=4 \\ y=7\end{array}\right.\)
(3)\(\left\{\begin{array}{l}x-2y=5 \\ 2x+3y=-4\end{array}\right.\)
\(\left\{\begin{array}{l}x=1 \\ y=-2\end{array}\right.\)
(4)\(\left\{\begin{array}{l}2x-y=9 \\ 3x+4y=8\end{array}\right.\)
\(\left\{\begin{array}{l}x=4 \\ y=-1\end{array}\right.\)
(5)\(\left\{\begin{array}{l}5x+3y=4 \\ 4x-3y=14\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=-2\end{array}\right.\)
(6)\(\left\{\begin{array}{l}-2x+3y=17 \\ 5x+9y=7\end{array}\right.\)
\(\left\{\begin{array}{l}x=-4 \\ y=3\end{array}\right.\)
(7)\(\left\{\begin{array}{l}2x-3y=-8 \\ 3x-4y=-9\end{array}\right.\)
\(\left\{\begin{array}{l}x=5 \\ y=6\end{array}\right.\)
(8)\(\left\{\begin{array}{l}8x-3y=-10 \\ 8x+2y=20\end{array}\right.\)
\(\left\{\begin{array}{l}x=1 \\ y=6\end{array}\right.\)
(9)\(\left\{\begin{array}{l}3x+2y=15 \\ 9x-5y=12\end{array}\right.\)
\(\left\{\begin{array}{l}x=3 \\ y=3\end{array}\right.\)
(10)\(\left\{\begin{array}{l}2x-3y=-14 \\ -5x+4y=28\end{array}\right.\)
\(\left\{\begin{array}{l}x=-4 \\ y=2\end{array}\right.\)
(11)\(\left\{\begin{array}{l}x+4y=14 \\ 2x-5y=-11\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=3\end{array}\right.\)
(12)\(\left\{\begin{array}{l}4x+y=3 \\ 7x+3y=4\end{array}\right.\)
\(\left\{\begin{array}{l}x=1 \\ y=-1\end{array}\right.\)
(13)\(\left\{\begin{array}{l}2x-5y=16 \\ 4x+7y=-2\end{array}\right.\)
\(\left\{\begin{array}{l}x=3 \\ y=-2\end{array}\right.\)
(14)\(\left\{\begin{array}{l}5x-3y=-7 \\ 11x+6y=-28\end{array}\right.\)
\(\left\{\begin{array}{l}x=-2 \\ y=-1\end{array}\right.\)
(15)\(\left\{\begin{array}{l}8x-3y=-18 \\ 2x+5y=-16\end{array}\right.\)
\(\left\{\begin{array}{l}x=-3 \\ y=-2\end{array}\right.\)
(16)\(\left\{\begin{array}{l}-7x+y=-11 \\ 3x-10y=-24\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=3\end{array}\right.\)
(17)\(\left\{\begin{array}{l}-6x+5y=19 \\ x-2y=-9\end{array}\right.\)
\(\left\{\begin{array}{l}x=1 \\ y=5\end{array}\right.\)
(18)\(\left\{\begin{array}{l}-6x+5y=40 \\ 3x-4y=-23\end{array}\right.\)
\(\left\{\begin{array}{l}x=-5 \\ y=2\end{array}\right.\)
(19)\(\left\{\begin{array}{l}x+4y=7 \\ 3x-10y=-12\end{array}\right.\)
\(\left\{\begin{array}{l}x=1 \\ \displaystyle y=\frac{3}{2}\end{array}\right.\)
(20)\(\left\{\begin{array}{l}9x+y=2 \\ 15x+2y=3\end{array}\right.\)
\(\left\{\begin{array}{l}\displaystyle x=\frac{1}{3} \\ y=-1\end{array}\right.\)
(21)\(\left\{\begin{array}{l}4x-3y=-5 \\ y=3x\end{array}\right.\)
\(\left\{\begin{array}{l}x=1 \\ y=3\end{array}\right.\)
(22)\(\left\{\begin{array}{l}2x+y=12 \\ x=-2y\end{array}\right.\)
\(\left\{\begin{array}{l}x=8 \\ y=-4\end{array}\right.\)
(23)\(\left\{\begin{array}{l}3x-2y=7 \\ x=y+4\end{array}\right.\)
\(\left\{\begin{array}{l}x=-1 \\ y=-5\end{array}\right.\)
(24)\(\left\{\begin{array}{l}2x+3y=13 \\ y=2x-1\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=3\end{array}\right.\)
(25)\(\left\{\begin{array}{l}-5x+2y=-8 \\ x=y-2\end{array}\right.\)
\(\left\{\begin{array}{l}x=4 \\ y=6\end{array}\right.\)
(26)\(\left\{\begin{array}{l}y=2x+1 \\ 3x-2y=-5\end{array}\right.\)
\(\left\{\begin{array}{l}x=3 \\ y=7\end{array}\right.\)
(27)\(\left\{\begin{array}{l}4x+y=3 \\ 7x+5y=-11\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=-5\end{array}\right.\)
(28)\(\left\{\begin{array}{l}3x-2y=2 \\ y=x+2\end{array}\right.\)
\(\left\{\begin{array}{l}x=6 \\ y=8\end{array}\right.\)
(29)\(\left\{\begin{array}{l}x=7-4y \\ 3x+8y=9\end{array}\right.\)
\(\left\{\begin{array}{l}x=-5 \\ y=3\end{array}\right.\)
(30)\(\left\{\begin{array}{l}x+9y=5 \\ -3x+5y=17\end{array}\right.\)
\(\left\{\begin{array}{l}x=-4 \\ y=1\end{array}\right.\)
(31)\(\left\{\begin{array}{l}x=-3y-7 \\ 2x+5y=-10\end{array}\right.\)
\(\left\{\begin{array}{l}x=5 \\ y=-4\end{array}\right.\)
(32)\(\left\{\begin{array}{l}y=3x-11 \\ 5x+2y=0\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=-5\end{array}\right.\)
(33)\(\left\{\begin{array}{l}3x+4y=6 \\ x=-3y+7\end{array}\right.\)
\(\left\{\begin{array}{l}x=-2 \\ y=3\end{array}\right.\)
(34)\(\left\{\begin{array}{l}3x-4y=-1 \\ y=2x+9\end{array}\right.\)
\(\left\{\begin{array}{l}x=-7 \\ y=-5\end{array}\right.\)
(35)\(\left\{\begin{array}{l}x=3y-29 \\ -5x-2y=-42\end{array}\right.\)
\(\left\{\begin{array}{l}x=4 \\ y=11\end{array}\right.\)
(36)\(\left\{\begin{array}{l}7x+5y=-21 \\ y=-4x+27\end{array}\right.\)
\(\left\{\begin{array}{l}x=12 \\ y=-21\end{array}\right.\)
(37)\(\left\{\begin{array}{l}x=-6y-7 \\ 3x+8y=-6\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ \displaystyle y=-\frac{3}{2}\end{array}\right.\)
(38)\(\left\{\begin{array}{l}y=3x-9 \\ 9x+2y=7\end{array}\right.\)
\(\left\{\begin{array}{l}\displaystyle x=\frac{5}{3} \\ y=-4\end{array}\right.\)
(39)\(\left\{\begin{array}{l}3x+10y=6 \\ x=-2y+1\end{array}\right.\)
\(\left\{\begin{array}{l}\displaystyle x=-\frac{1}{2} \\ \displaystyle y=\frac{3}{4}\end{array}\right.\)
(40)\(\left\{\begin{array}{l}2x-5y=-9 \\ y=-2x-1\end{array}\right.\)
\(\left\{\begin{array}{l}\displaystyle x=-\frac{7}{6} \\ \displaystyle y=\frac{4}{3}\end{array}\right.\)
(41)\(\left\{\begin{array}{l}2(x+y)-3y=6 \\ x+y=6\end{array}\right.\)
\(\left\{\begin{array}{l}x=4 \\ y=2\end{array}\right.\)
(42)\(\left\{\begin{array}{l}3x-5(x-y)=-22 \\ 2x+y=10\end{array}\right.\)
\(\left\{\begin{array}{l}x=6 \\ y=-2\end{array}\right.\)
(43)\(\left\{\begin{array}{l}2x+y=1 \\ x+3(x+y)=7\end{array}\right.\)
\(\left\{\begin{array}{l}x=-2 \\ y=5\end{array}\right.\)
(44)\(\left\{\begin{array}{l}2(4x-y)+5y=13 \\ 4x+y=3\end{array}\right.\)
\(\left\{\begin{array}{l}x=-1 \\ y=7\end{array}\right.\)
(45)\(\left\{\begin{array}{l}3x+2(x-3y)=-9 \\ x+y=7\end{array}\right.\)
\(\left\{\begin{array}{l}x=3 \\ y=4\end{array}\right.\)
(46)\(\left\{\begin{array}{l}-5(3x-4)=y+1 \\ 2x-5y-10=4(x-2y)\end{array}\right.\)
\(\left\{\begin{array}{l}x=1 \\ y=4\end{array}\right.\)
(47)\(\left\{\begin{array}{l}3(3x-2y)=8(2x+y) \\ 2x+3=x+2y-1\end{array}\right.\)
\(\left\{\begin{array}{l}x=-2 \\ y=1\end{array}\right.\)
(48)\(\left\{\begin{array}{l}4(3x-y)=5x-13y+15 \\ x-y=-(2x+8y)-3\end{array}\right.\)
\(\left\{\begin{array}{l}x=6 \\ y=-3\end{array}\right.\)
(49)\(\left\{\begin{array}{l}7x=2(-3x+8y)+9 \\ -4(2x+3y)=60\end{array}\right.\)
\(\left\{\begin{array}{l}x=-3 \\ y=-3\end{array}\right.\)
(50)\(\left\{\begin{array}{l}4x-3y-2=2(x+y-5) \\ -(2x-7y)=12\end{array}\right.\)
\(\left\{\begin{array}{l}x=1 \\ y=2\end{array}\right.\)
(51)\(\left\{\begin{array}{l}0.5x+0.6y=1.3 \\ x+3y=8\end{array}\right.\)
\(\left\{\begin{array}{l}x=-1 \\ y=3\end{array}\right.\)
(52)\(\left\{\begin{array}{l}0.3x-0.2y=-1.8 \\ x-2y=-10\end{array}\right.\)
\(\left\{\begin{array}{l}x=-4 \\ y=3\end{array}\right.\)
(53)\(\left\{\begin{array}{l}0.4x-0.5y=-1.2 \\ x+2y=10\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=4\end{array}\right.\)
(54)\(\left\{\begin{array}{l}x-4y=9 \\ 0.3x-0.8y=1.1\end{array}\right.\)
\(\left\{\begin{array}{l}x=-7 \\ y=-4\end{array}\right.\)
(55)\(\left\{\begin{array}{l}0.6x+1.5y=-1.8 \\ 2.1x-0.5y=5.2\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=-2\end{array}\right.\)
(56)\(\left\{\begin{array}{l}2.1x-1.3y=-1.1 \\ 5.2x+0.9y=-19.2\end{array}\right.\)
\(\left\{\begin{array}{l}x=-3 \\ y=-4\end{array}\right.\)
(57)\(\left\{\begin{array}{l}4.8x-3.2y=30.4 \\ 10.5x+8.4y=35.7\end{array}\right.\)
\(\left\{\begin{array}{l}x=5 \\ y=-2\end{array}\right.\)
(58)\(\left\{\begin{array}{l}0.01x-1.02y=-4.11 \\ 0.3x-2.1y=-9.3\end{array}\right.\)
\(\left\{\begin{array}{l}x=-3 \\ y=4\end{array}\right.\)
(59)\(\left\{\begin{array}{l}-1.04x+2.04y=20.52 \\ 1.4x+0.8y=-2.8\end{array}\right.\)
\(\left\{\begin{array}{l}x=-6 \\ y=7\end{array}\right.\)
(60)\(\left\{\begin{array}{l}10.8x+10.2y=13.2 \\ 0.03x-0.24y=1.11\end{array}\right.\)
\(\left\{\begin{array}{l}x=5 \\ y=-4\end{array}\right.\)
(61)\(\left\{\begin{array}{l}\displaystyle \frac{3}{8}x+\frac{y}{4}=2 \\ x-y=-3\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=5\end{array}\right.\)
(62)\(\left\{\begin{array}{l}\displaystyle \frac{5}{6}x-\frac{4}{3}y=4 \\ x-y=6\end{array}\right.\)
\(\left\{\begin{array}{l}x=8 \\ y=2\end{array}\right.\)
(63)\(\left\{\begin{array}{l}-3x+2y=1 \\ \displaystyle \frac{x}{3}-\frac{2}{5}y=-1\end{array}\right.\)
\(\left\{\begin{array}{l}x=3 \\ y=5\end{array}\right.\)
(64)\(\left\{\begin{array}{l}\displaystyle -\frac{5}{4}x+\frac{y}{3}=-\frac{1}{2} \\ 7x-y=8\end{array}\right.\)
\(\left\{\begin{array}{l}x=2 \\ y=6\end{array}\right.\)
(65)\(\left\{\begin{array}{l}\displaystyle 4x-\frac{3}{2}y=-1 \\ \displaystyle \frac{4}{3}x-\frac{4}{3}y=\frac{4}{3}\end{array}\right.\)
\(\left\{\begin{array}{l}x=-1 \\ y=-2\end{array}\right.\)
(66)\(\left\{\begin{array}{l}\displaystyle \frac{2}{3}x+\frac{5}{3}y=\frac{4}{3} \\ \displaystyle -\frac{4}{3}x+2y=8\end{array}\right.\)
\(\left\{\begin{array}{l}x=-3 \\ y=2\end{array}\right.\)
(67)\(\left\{\begin{array}{l}\displaystyle \frac{1}{4}x-\frac{1}{2}y=-\frac{3}{4} \\ \displaystyle x+\frac{1}{6}y=\frac{17}{3}\end{array}\right.\)
\(\left\{\begin{array}{l}x=5 \\ y=4\end{array}\right.\)
(68)\(\left\{\begin{array}{l}\displaystyle \frac{1}{6}x+\frac{5}{6}y=\frac{31}{6} \\ \displaystyle 2x-\frac{1}{10}y=\frac{7}{5}\end{array}\right.\)
\(\left\{\begin{array}{l}x=1 \\ y=6\end{array}\right.\)
(69)\(\left\{\begin{array}{l}\displaystyle \frac{2}{5}x-\frac{1}{5}y=-2 \\ \displaystyle -\frac{4}{3}x+\frac{5}{3}y=\frac{32}{3}\end{array}\right.\)
\(\left\{\begin{array}{l}x=-3 \\ y=4\end{array}\right.\)
(70)\(\left\{\begin{array}{l}\displaystyle \frac{1}{4}x-\frac{3}{2}y=4 \\ \displaystyle \frac{5}{9}x-\frac{1}{3}y=-\frac{1}{9}\end{array}\right.\)
\(\left\{\begin{array}{l}x=-2 \\ y=-3\end{array}\right.\)
(71)\(2x+y=-x+3y=7\)
\(\left\{\begin{array}{l}x=2 \\ y=3\end{array}\right.\)
(72)\(x-3y=3x-y-6=7\)
\(\left\{\begin{array}{l}x=4 \\ y=-1\end{array}\right.\)
(73)\(5x+y=-x-2y=9\)
\(\left\{\begin{array}{l}x=3 \\ y=-6\end{array}\right.\)
(74)\(7x-y=-3x+2y+5=9\)
\(\left\{\begin{array}{l}x=2 \\ y=5\end{array}\right.\)
(75)\(x+2y=2x+3y-8=15\)
\(\left\{\begin{array}{l}x=1 \\ y=7\end{array}\right.\)
(76)\(x-3y=5x+3y=4x-y+5\)
\(\left\{\begin{array}{l}x=-3 \\ y=2\end{array}\right.\)
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