A )x+y=4 x+2y=6 b) 2x-4y=2 x+y=4 c) y-x=2 x+2y=11 d) x-2=-1 2x=y e) x-3=0 2x+y=4 f) 3x+2y=8 3/4y=3 g.... Question from @Dynamyte

rk1993 A) x + 2y = 6 / * 2
2x - 4y = 2

2x + 4y = 12
2x - 4y = 2
4x = 14 / : 4
x = 2,5

2,5 + 2y = 6
2y = 3,5 / : 2
y = 1,75 a więc ( x = 2,5 ; y = 1,75 )

b) 2x-4y=2
x+y=4 / * 4

2x - 4y = 2
4x + 4y = 16
6x = 18 / : 6
x = 3
2 * 3 - 4y = 2
-4y = -4
y = 1 a więc ( x = 3 ; y = 1 )

c) y-x=2
x+2y=11
-x + y = 2
x + 2y = 11
3y = 13 / :3
y = 13/3
13/3 - x = 2
-x = -7/3
x = 7/3 a więc ( x = 7/3 : y 13/3 )

d) x-2=-1
2x=y

x = 1
y = 2

e) x-3=0
2x+y=4

x = 3
2 * 3 + y = 4
y = -2 a więc ( x = 3 : y = -2 )

f) 3x+2y=8
3/4y=3 / * 4/3
y = 4
3x + 2 * 4 = 8
3x = 0
x = 0 a więc ( x = 0 ; y = 4 )

g) 2x +y=3
x-y=9
3x = 12
x = 4
4 - y = 9
-y = 5
y = -5 a więc ( x = 4 ; y = -5)

h) 3x-2y=3
3x+y=3/2 / * 2

3x - 2y = 3
6x + 2y = 3
9x = 6
x = 2/3
3 * 2/3 - 2y = 3
-2y = 1
y = - 1/2 a więc ( x = 2/3 ; y = -1/2 )

i) 8x+16y=24/:8
3x-5y=-2

x + 2y = 3 / * -3
3x - 5y = -2

-3x - 6y = -9
3x - 5y = -2
-11y = -11
y = 1
x + 2 = 3
x = 1 a więc ( x = 1 ; y = 1 )

j) 5x+10y=5
3y-2x=12

5x + 10y = 5 / * 2
-2x + 3y = 12 / * 5

10x + 20y = 10
-10x + 15y = 60
35y = 70
y = 2
5x + 20 = 5
5x = -15
x = -3 a więc ( x = -3 ; y = 2 )

k) 2x+3y=20
-x+3y=-1 / * 2
2x + 3y = 20
-2x + 6y = -2
9y = 18
y = 2
2x + 3 * 2 = 20
2x = 14
x = 7 a więc ( x = 7 ; y = 2 )

1 votes Thanks 1

olciax95 $A)\\ \left \{ {{x+y=4} \atop {x+2y=6}} \right. \\\left \{ {{-x-y=-4} \atop {x+2y=6}} \right. \\y=2\\x+2=4\\x=2\\\\
B)\\ \left \{ {{2x-4y=2} \atop {x+y=4}} \right. \\\left \{ {{2x-4y=2} \atop {-2x-2y=-8}} \right.\\-6y=-6\\y=1\\x+1=4\\x=3$

$C)\\ \left \{ {{y-x=2} \atop {x+2y=11}} \right. \\3y=13\\y=\frac{13}{3}=4\frac{1}{3}\\4\frac{1}{3}-x=2\\4\frac{1}{3}-2=x\\2\frac{1}{3}=x\\\\ D) \\\left \{ {{x-2=-1} \atop {2x=y}} \right. \\\left \{ {{x=1} \atop {y=2}}$

$E)\\ \left \{ {{x-3=0} \atop {2x+y=4}} \right. \\\left \{ {{x=3} \atop {6+y=4}} \right. \\\left \{ {{x=3} \atop {y=-2}} \right. \\ \\\\
F)\\ \left \{ {{3x+2y=8} \atop {\frac{3}{4}y=3}} \right. \\ \left \{ {{3x+2y=8} \atop {y=4}} \right. \\ \left \{ {{3x+8=8} \atop {y=4}} \right.\\ \left \{ {{3x=0} \atop {y=4}} \right.\\ \left \{ {{x=0} \atop {y=4}} \right.$

$G)\\ \left \{ {{2x+y=3} \atop {x-y=9}} \right. \\3x=12\\x=4\\4-y=9\\-y=5\\y=-5\\\\\\
H)\\ \left \{ {{3x-2y=3} \atop {3x+y=\frac{3}{2}}} \right. \\\left \{ {{-3x+2y=-3} \atop {3x+y=\frac{3}{2}}} \right. \\3y=-\frac{3}{2}\\y=y=-\frac{1}{2}\\3x-\frac{1}{2}=\frac{3}{2}\\3x=2\\x=\frac{2}{3}$

$I)\\ \left \{ {{8x+16y=24} \atop {3x-5y=-2}} \right. \\ \left \{ {{x+2y=3} \atop {3x-5y=-2}} \right. \\ \left \{ {{x=-2y+3} \atop {3(-2y+3)-5y=-2}} \right. \\ \left \{ {{x=-2y+3} \atop {-6y+9-5y=-2}} \right. \\ \left \{ {{x=-2y+3} \atop {-11y=-11}} \right.\\ \left \{ {{y=1} \atop {x=-2+3}} \right.\\ \left \{ {{y=1} \atop {x=1}} \right.$

$J)\\ \left \{ {{5x+10y=5} \atop {3y-2x=12}} \right. \\\left \{ {{10x+20y=10} \atop {-10x+15y=60}} \right. \\35y=70\\y=2\\5x+20=5\\5x=-15\\x=-3\\\\K)\\ \left \{ {{2x+3y=20} \atop {-x+3y=-1}} \right. \\\left \{ {{2x+3y=20} \atop {x-3y=1}} \right. \\3x=21\\x=7\\-7+3y=-1\\3y=6\\y=\frac{6}{3}=2$

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