3x-4y=13
2x+3y=3
solve this simultaneous equations? 3x-4y=13 2x+3y=3?
2008-04-18 1:06 pm
回答 (13)
2008-04-18 1:17 pm
✔ 最佳答案
3x-4y=13multiplying by 3 9x-12y=39....................(1)
2x+3y=3
multiplying by 4 8x+12y=12....................(2)
adding 1 and 2
17x=51
so x=51/17 =>3
substituting in 3x-4y=13 and solving -4y=4 and so y=-1
2008-04-18 1:41 pm
Values of y:
3x - 4y = 13
4y = 3x - 13
y = (3x - 13)/4
2x + 3y = 3
3y = 3 - 2x
y = (3 - 2x)/3
Value of x:
3(3x - 13) = 4(3 - 2x)
9x - 39 = 12 - 8x
17x = 51
x = 3
Value of y:
= (3[3] - 13)/4
= (9 - 13)/4
= - 4/4
= - 1
Answer: x = 3, y = - 1
Check (1st equation):
3(3) - 4(- 1) = 13
9 + 4 = 13
Check (2nd equation):
2(3) + 3(- 1) = 3
6 - 3 = 3
3x - 4y = 13
4y = 3x - 13
y = (3x - 13)/4
2x + 3y = 3
3y = 3 - 2x
y = (3 - 2x)/3
Value of x:
3(3x - 13) = 4(3 - 2x)
9x - 39 = 12 - 8x
17x = 51
x = 3
Value of y:
= (3[3] - 13)/4
= (9 - 13)/4
= - 4/4
= - 1
Answer: x = 3, y = - 1
Check (1st equation):
3(3) - 4(- 1) = 13
9 + 4 = 13
Check (2nd equation):
2(3) + 3(- 1) = 3
6 - 3 = 3
2013-09-25 2:14 am
3x - 4y = 13
2x + 3y = 3
Solution:
x = 3, y = -1
2x + 3y = 3
Solution:
x = 3, y = -1
參考: http://www.wolframalpha.com/input/?i=3x-4y=13, 2x+3y=3
2008-04-18 2:27 pm
3x - 4y = 13
3x = 13 + 4y
x = (13 + 4y)/3
2x = 2(13 + 4y)/3
2x + 3y = 3
2(13 + 4y)/3 + 3y = 3
(26 + 8y)/3 + 3y = 3
3[(26 + 8y)/3 + 3y] = 3(3)
26 + 8y + 9y = 9
17y = 9 - 26
17y = -17
y = -17/17
y = -1
3x - 4y = 13
3x - 4(-1) = 13
3x = 13 - 4
3x = 9
x = 9/3
x = 3
∴ x = 3 , y = -1
3x = 13 + 4y
x = (13 + 4y)/3
2x = 2(13 + 4y)/3
2x + 3y = 3
2(13 + 4y)/3 + 3y = 3
(26 + 8y)/3 + 3y = 3
3[(26 + 8y)/3 + 3y] = 3(3)
26 + 8y + 9y = 9
17y = 9 - 26
17y = -17
y = -17/17
y = -1
3x - 4y = 13
3x - 4(-1) = 13
3x = 13 - 4
3x = 9
x = 9/3
x = 3
∴ x = 3 , y = -1
2008-04-18 2:09 pm
3x-4y=13 (1)
2x+3y=3 (2)
6x-8y=26 (1)X2 (3)
6x+9y=9 (2)X3 (4)
17y= -17 (4)-(3)
y = -1 implies x = 3
2x+3y=3 (2)
6x-8y=26 (1)X2 (3)
6x+9y=9 (2)X3 (4)
17y= -17 (4)-(3)
y = -1 implies x = 3
2008-04-18 1:24 pm
to solve this problem use elimination or substitution ok
i'm using elimination
3x - 4y = 15.........(1)
2x + 3y = 3............(2)
(1) x 3 ......> 9x - 12y = 39
(2) x 4......> 8x +12y = 12
------------------------------------------ +
so 17 x = 51
x = 3 .........(4)
(4) ..> (2) ..... 2x + 3y = 3
2.3 + 3y = 3
3y = 3 - 6
y = - 3/3
y = - 1
solution value of x = 3 and
y = -1
i'm using elimination
3x - 4y = 15.........(1)
2x + 3y = 3............(2)
(1) x 3 ......> 9x - 12y = 39
(2) x 4......> 8x +12y = 12
------------------------------------------ +
so 17 x = 51
x = 3 .........(4)
(4) ..> (2) ..... 2x + 3y = 3
2.3 + 3y = 3
3y = 3 - 6
y = - 3/3
y = - 1
solution value of x = 3 and
y = -1
2008-04-18 1:21 pm
-2(3x-4y=13)
3(2x+3y=3)
===>
-6x+8y=-26
6x+9y= 9
using elemination:
17y=-17 ===> y=-1
sub in any equation:
3x= 13+ 4(-1)
3x=9
x=3
(3,-1)
3(2x+3y=3)
===>
-6x+8y=-26
6x+9y= 9
using elemination:
17y=-17 ===> y=-1
sub in any equation:
3x= 13+ 4(-1)
3x=9
x=3
(3,-1)
2008-04-18 1:20 pm
6x-8y= 26,( multiply eq1 by 2), 6x+9y= 9( multiply eq2 by 3)
subtracting eq 2 from eq 1 is -17 y= 17 therefore y=-1
substituting y= -1, x = 3
subtracting eq 2 from eq 1 is -17 y= 17 therefore y=-1
substituting y= -1, x = 3
2008-04-18 1:19 pm
You can use substitution but I would recommend subtraction:
Multiply Equation 1 by 2, getting:
6x - 8y = 26
Then multiply Equation 2 by 3, getting:
6x + 9y = 9
Subtract Equation 2 from Equation 1, getting:
-17y = 17, which means y = -1
Substitute that value of "y" into either original equation, getting (e.g.,): 2x + 3(-1) = 3 or 2x -3 = 3 or 2x = 6
So x=3 and y=-1
Multiply Equation 1 by 2, getting:
6x - 8y = 26
Then multiply Equation 2 by 3, getting:
6x + 9y = 9
Subtract Equation 2 from Equation 1, getting:
-17y = 17, which means y = -1
Substitute that value of "y" into either original equation, getting (e.g.,): 2x + 3(-1) = 3 or 2x -3 = 3 or 2x = 6
So x=3 and y=-1
2008-04-18 1:17 pm
Easy. 3x -4y = 13. expand this to 6x - 8y = 26. Name this Eqn1.
Expand 2x + 3y = 3 to 6x + 9y = 9. Name this Eqn2. Then:
Eqn1 - Eqn2
6x - 8y - 6x - 9y = 26 - 9
-17y = 17
y = -1
Subst. y = -1 into Eqn2.
2x - 3 = 3
x = 6/2 = 3.
x = 3, y = -1
Expand 2x + 3y = 3 to 6x + 9y = 9. Name this Eqn2. Then:
Eqn1 - Eqn2
6x - 8y - 6x - 9y = 26 - 9
-17y = 17
y = -1
Subst. y = -1 into Eqn2.
2x - 3 = 3
x = 6/2 = 3.
x = 3, y = -1
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