# wQN Q A

#### PDẢ

𓚂\ɂꍇ́Ã{^ĂB

(1) ̘A@ŉ܂傤B
(1)$y=3x$
$5x+y=16$

(2)$2x-3y=-8$
$x=4y+1$

(3)$y=x+1$
$y=-2x+13$

(4)$9x+y=24$
$x=3y-16$

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

(6)$4x+3y=7$
$3y=-7x+10$

(7)$2x-7y=3$
$x-3y=2$

(8)$4x-y=-8$
$2x+3y=3$

(1)$y=3x$  ……①
$5x+y=16$  ……②

①②ɑ
$5x+3x=16$
$8x=16$
$x=2$
①ɑ
$y=3\times 2=6$
ij$x=2$  ,$y=6$

(2)$2x-3y=-8$  ……①
$x=4y+1$  ……②

②①ɑ
$2\left( 4y+1 \right)-3y=-8$
$8y+2-3y=-8$
$5y=-10$
$y=-2$
②ɑ
$x=4\times \left( -2 \right)+1=-7$
ij$x=-7$  ,$y=-2$

(3)$y=x+1$  ……①
$y=-2x+13$  ……②

①②ɑ
$x+1=-2x+13$
$x+2x=13-1$
$3x=12$
$x=4$
①ɑ
$y=4+1=5$
ij$x=4$  ,$y=5$

(4)$9x+y=24$  ……①
$x=3y-16$  ……②

②①ɑ
$9\left( 3y-16 \right)+y=24$
$27y-144+y=24$
$28y=168$
$y=6$
②ɑ
$x=3\times 6-16=2$
ij$x=2$  ,$y=6$

(5)$x=2y+5$  ……①
$y=x-3$  ……②

②①ɑ
$x=2\left( x-3 \right)+5$
$x=2x-6+5$
$x=1$
②ɑ
$y=1-3=-2$
ij$x=1$  ,$y=-2$

(6)$4x+3y=7$  ……①
$3y=-7x+10$  ……②

②①ɑ
$4x+\left( -7x+10 \right)=7$
$4x-7x+10=7$
$3x=3$
$x=1$
②ɑ
$3y=-7\times 1+10$
$y=1$
ij$x=1$  ,$y=1$

(7)$2x-7y=3$  ……①
$x-3y=2$  ……②

②ό$x=3y+2$  ……③
③①ɑ
$2\left( 3y+2 \right)-7y=3$
$6y+4-7y=3$
$y=1$
③ɑ
$x=3\times 1+2=5$
ij$x=5$  ,$y=1$

(8)$4x-y=-8$  ……①
$2x+3y=3$  ……②

①ό$y=4x+8$  ……③
③②ɑ
$2x+3\left( 4x+8 \right)=3$
$2x+12x+24=3$
$14x=-21$
$x=-\dfrac {3} {2}$
③ɑ
$y=4\times \left( -\dfrac {3} {2} \right)+8=2$
ij$x=-\dfrac {3} {2}$  ,$y=2$

(2) ̘A@ŉ܂傤B
(1)$2x-3y=9$
$2x-5y=11$

(2)$7x+2y=23$
$3x+2y=19$

(3)$3x-5y=21$
$8x+5y=1$

(4)$5x-9y=19$
$-5x+6y=-13$

(5)$5x+4y=42$
$3x+y=21$

(6)$x+4y=16$
$3x+5y=13$

(7)$2x-y=4$
$7x-3y=15$

(8)$2x-3y=-7$
$-x+4y=6$

(1)$2x-3y=9$  ……①
$2x-5y=11$  ……②

①|②
Q|R X
|j Q|TPP
Q|Q

$y=-1$  ……③
③①ɑāA
$2x-3\times \left( -1 \right)=9$
$2x=6$
$x=3$
ij$x=3$  ,$y=-1$

(2)$7x+2y=23$  ……①
$3x+2y=19$  ……②

①|②
V{QQR
|j R{QPX
S    S

$x=1$  ……③
③②ɑāA
$3\times 1+2y=19$
$2y=16$
$y=8$
ij$x=1$  ,$y=8$

(3)$3x-5y=21$  ……①
$8x+5y=1$  ……②

①{②
R|TQP
{j W{T P
PP   QQ

$x=2$  ……③
③①ɑāA
$3\times 2-5y=21$
$5y=-15$
$y=-3$
ij$x=2$  ,$y=-3$

(4)$5x-9y=19$  ……①
$-5x+6y=-13$  ……②

①{②
T|X PX
{j |T{U|PR
|R  U

$y=-2$  ……③
③①ɑāA
$5x-9\times \left( -2 \right)=19$
$5x=1$
$x=\dfrac {1} {5}$
ij$x=\dfrac {1} {5}$  ,$y=-2$

(5)$5x+4y=42$  ……①
$3x+y=21$  ……②

①|②~S
T{SSQ
|j PQ{SWQ
|V   |SQ

$x=6$  ……③
③②ɑāA
$3\times 6+y=21$
$y=3$
ij$x=6$  ,$y=-2$

(6)$x+4y=16$  ……①
$3x+5y=13$  ……②

①~R|②
R{PQSW
|j R{ TPR
VRT

$y=5$  ……③
③①ɑāA
$x+4\times 5=16$
$x=-4$
ij$x=-4$  ,$y=5$

(7)$2x-y=4$  ……①
$7x-3y=15$  ……②

①~R|②
U|RPQ
|j V|RPT
|   |R

$x=3$  ……③
③①ɑāA
$2\times 3-y=4$
$y=2$
ij$x=3$  ,$y=2$

(8)$2x-3y=-7$  ……①
$-x+4y=6$  ……②

①{②~Q
Q|R|V
{j |Q{WPQ
TT

$y=1$  ……③
③②ɑāA
$-x+4\times 1=6$
$x=-2$
ij$x=-2$  ,$y=1$

(3) ̘A܂傤B
(1)$3x-2y=-7$
$x=3y$

(2)$y=2x-10$
$7x-2y=29$

(3)$2x+4y=16$
$6x+5y=27$

(4)$-2x+9y=30$
$5x+3y=-24$

(5)$2x+3y=2$
$3x+2y=-7$

(6)$3x-2y=12$
$2y=x-8$

(7)$14x+9y=5$
$21x-3y=24$

(8)$5x+9y=-19$
$2x+6y=-10$

(1)$3x-2y=-7$  ……①
$x=3y$  ……②

@p܂B
②①ɑ
$3\times 3y-2y=-7$
$9y-2y=-7$
$7y=-7$
$y=-1$  ……③
③②ɑāA
$x=3\times \left( -1 \right)=-3$
ij$x=-3$  ,$y=-1$

(2)$y=2x-10$  ……①
$7x-2y=29$  ……②

@p܂B
①②ɑ
$7x-2\left( 2x-10 \right)=29$
$7x-4x+20=29$
$3x=9$
$x=3$  ……③
③①ɑāA
$y=2\times 3-10=-4$
ij$x=3$  ,$y=-4$

(3)$2x+4y=16$  ……①
$6x+5y=27$  ……②

@p܂B
①~R|②
U{PQSW
|j  U{ TQV
VQP

$y=3$  ……③
③①ɑāA
$2\times x+4\times 3=16$
$2x=4$
$x=2$
ij$x=2$  ,$y=3$

(4)$-2x+9y=30$  ……①
$5x+3y=-24$  ……②

@p܂B
①|②~R
|Q{X RO
|j  PT{X|VQ
|PV   POQ

$x=-6$  ……③
③①ɑāA
$-2\times \left( -6 \right)+9y=30$
$9y=18$
$y=2$
ij$x=-6$  ,$y=2$

(5)$2x+3y=2$  ……①
$3x+2y=-7$  ……②

@p܂B
①~R|②~Q
U{X  U
|j  U{S|PS
T QO

$y=4$  ……③
③②ɑāA
$3x+2\times 4=-7$
$3x=-15$
$x=-5$
ij$x=-5$  ,$y=4$

(6)$3x-2y=12$  ……①
$2y=x-8$  ……②

@p܂B
②①ɑāA
$3x-\left( x-8 \right)=12$
$3x-x+8=12$
$2x=4$
$x=2$  ……③
③②ɑāA
$2y=2-8=-6$
$y=-3$
ij$x=2$  ,$y=-3$

(7)$14x+9y=5$  ……①
$21x-3y=24$  ……②

@p܂B
①{②~R
PS{X T
{j  UR|XVQ
VV    VV

$x=1$  ……③
③①ɑāA
$14\times 1+9y=5$
$9y=-9$
$y=-1$
ij$x=1$  ,$y=-1$

(8)$5x+9y=-19$  ……①
$2x+6y=-10$  ……②

@p܂B
①~Q|②~T
PO{PW|RW
|j  PO{RO|TO
|PQ PQ

$y=-1$  ……③
③②ɑāA
$2x+6\times \left( -1 \right)=-10$
$2x=-10+6$
$x=-2$
ij$x=-2$  ,$y=-1$

(4) ̘A܂傤B
(1)$3.5x+2.5y=4.5$
$0.7x-0.8y=2.2$

(2)$1.6x-0.9y=3$
$2.8x+1.8y=12$

(3)$\dfrac {2} {3} x+\dfrac {5} {2} y=-6$
$\dfrac {5} {6} x-\dfrac {3} {4} y=8$

(4)$\dfrac {1} {4} x-\dfrac {5} {8} y=\dfrac {1} {8}$
$\dfrac {1} {2} x-\dfrac {3} {4} y=-\dfrac {1} {4}$

(5)$2x-3y=3$
$2\left( x+4 \right)=7-y$

(6)$3\left( x-y \right)+2y=11$
$5x-3\left( 2x-y \right)=-9$

(1)$3.5x+2.5y=4.5$  ……①
$0.7x-0.8y=2.2$  ……②

①~PO$35x+25y=45$  ……③
②~PO$7x-8y=22$  ……④

④~T$35x-40y=110$  ……⑤

③|⑤
RT{QT ST
|j  RT|SOPPO
UT|UT

$y=-1$  ……⑥
⑥④ɑ
$7x-8\times \left( -1 \right)=22$
$7x=14$
$x=2$
ij$x=2$  ,$y=-1$

(2)$1.6x-0.9y=3$  ……①
$2.8x+1.8y=12$  ……②
①~PO$16x-9y=30$  ……③
②~PO$28x+18y=120$  ……④

①~Q$32x-18y=60$  ……⑤

⑤{④
RQ|PW UO
{j  QW{PWPQO
UO   PWO

$x=3$  ……⑥
⑥③ɑ
$16\times 3-9y=30$
$9y=18$
$y=2$
ij$x=3$  ,$y=2$

(3)$\dfrac {2} {3} x+\dfrac {5} {2} y=-6$  ……①
$\dfrac {5} {6} x-\dfrac {3} {4} y=8$  ……②

①~U$4x+15y=-36$  ……③
②~PQ$10x-9y=96$  ……④

③~T$20x+75y=-180$  ……⑤
④~Q$20x-18y=192$  ……⑥

⑤|⑥
QO{VT|PWO
|j  QO|PW PXQ
XR|RVQ

$y=-4$  ……⑦
⑦③ɑāA
$4x+15\times \left( -4 \right)=-36$
$4x-60=-36$
$4x=24$
$x=6$
ij$x=6$  ,$y=-4$

(4)$\dfrac {1} {4} x-\dfrac {5} {8} y=\dfrac {1} {8}$  ……①
$\dfrac {1} {2} x-\dfrac {3} {4} y=-\dfrac {1} {4}$  ……②

①~W$2x-5y=1$  ……③
②~S$2x-3y=-1$  ……④

③|④
Q|T P
|j  Q|R|P
|QQ

$y=-1$  ……⑤
⑤③ɑ
$2x-5\times \left( -1 \right)=1$
$2x+5=1$
$2x=-4$
$x=-2$
ij$x=-2$  ,$y=-1$

(5)$2x-3y=3$  ……①
$2\left( x+4 \right)=7-y$  ……②

②ό$2x+y=-1$  ……③

①|③
Q|R R
|j  Q{ |P
|SS

$y=-1$  ……④
④③ɑ
$2x+\left( -1 \right)=1$
$2x=2$
$x=1$
ij$x=1$  ,$y=-1$

(6)$3\left( x-y \right)+2y=11$  ……①
$5x-3\left( 2x-y \right)=-9$  ……②

①ό$3x-y=11$  ……③
②ό$-x+3y=-9$  ……④

③{④~R
R|  PP
{j  R{X|QV
W|PU

$y=-2$  ……⑤
⑤④ɑāA
$-x+3\times \left( -2 \right)=-9$
$x=3$
ij$x=3$  ,$y=-2$

(5) ̘A܂傤B
(1)$3x-5y+4=-2x+3y=2$

(2)$8-3x=-5x+3y=2x+5y+3$

(3)$x+y-3z=-1$
$x-y+2z=6$
$2x+y-z=4$

(4)$2x-4y-3z=-2$
$3x+2y+3z=-4$
$2x-5y-6z=-6$

(5)$x:\left( x+y \right)=2:5$
$3x-y=6$

(6)$\left( x+y \right):\left( x-y \right)=3:2$
$4x+y=21$

(1)$3x-5y+4=-2x+3y=2$

$3x-5y+4=2$  ……①
$-2x+3y=2$  ……②

①ό$3x-5y=-2$  ……③

③~Q{②~R
U|PO|S
{j  |U{ X U
|Q

$y=-2$  ……④
④②ɑ
$-2x+3\times \left( -2 \right)=2$
$-2x=8$
$x=-4$
ij$x=-4$  ,$y=-2$

(2)$8-3x=-5x+3y=2x+5y+3$

$8-3x=-5x+3y$  ……①
$-5x+3y=2x+5y+3$  ……②

①ό$-2x+3y=8$  ……③
②ό$-7x-2y=3$  ……④

③~Q{④~R
|S{UPU
{j  |QP|U X
|QT  QT

$x=-1$  ……⑤
⑤③ɑ
$-2\times \left( -1 \right)+3y=8$
$3y=6$
$y=2$
ij$x=-1$  ,$y=2$

(3)$x+y-3z=-1$  ……①
$x-y+2z=6$  ……②
$2x+y-z=4$  ……③

①{②
$2x-z=5$  ……④

②{③
$3x+z=10$  ……⑤

④{⑤
$5x=15$
$x=3$  ……⑥

⑥⑤ɑ
$3\times 3+z=10$
$z=1$  ……⑦

⑥⑦①ɑ
$3+y-3\times 1=-1$
$y=-1$
ij$x=3$  ,$y=-1$  ,$z=1$

(4)$2x-4y-3z=-2$  ……①
$3x+2y+3z=-4$  ……②
$2x-5y-6z=-6$  ……③

①{②
$5x-2y=-6$  ……④

②~Q{③
$8x-y=-14$  ……⑤

④|⑤~Q
$-11x=22$
$x=-2$  ……⑥

⑥⑤ɑ
$8\times \left( -2 \right)-y=-14$
$y=-2$  ……⑦

⑥⑦①ɑ
$2\times \left( -2 \right)-4\times \left( -2 \right)-3z=-2$
$-3z=-6$
$z=2$
ij$x=-2$  ,$y=-2$  ,$z=2$

(5)$x:\left( x+y \right)=2:5$  ……①
$3x-y=6$  ……②

①ό
$5x=2\left( x+y \right)$
$3x=2y$  ……③

③②ɑ
$2y-y=6$
$y=6$  ……④

④③ɑ
$3x=2\times 6$
$x=4$
ij$x=4$  ,$y=6$

(6)$\left( x+y \right):\left( x-y \right)=3:2$  ……①
$4x+y=21$  ……②

①ό
$2\left( x+y \right)=3\left( x-y \right)$
$x=5y$  ……③

③②ɑ
$4\times 5y+y=21$
$21y=21$
$y=1$  ……④

④③ɑ
$x=5\times 1$
$x=5$
ij$x=5$  ,$y=1$