4x+6y=15 3x-4y=7 solve by substitution method
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4x+6y=15, 3x-4y=7 solve using substitution method?
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alpha's avatar
alpha
Lv 7
1 decade ago
Favorite Answer
[02]
4x+6y=15......(1)
3x-4y=7.........(2)
from 1 we get,
4x=15-6y
x=(15-6y)/4
substituting x by (15-6y)/4 in eqn 2
3(15-6y)/4 -4y=7
Multiplying both sides by 4
3(15-6y)-16y=28
45-18y-16y=28
-34y=28-45= -17
y= -17/-34=1/2
Plugging y in 1,we get
4x+3=15
4x=15-3=12
x=12/4=3
x=3 and y=1/2 ans
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11
Jun Agruda's avatar
Jun Agruda
Lv 7
1 decade ago
Relative values of y:
4x + 6y = 15
6y = 15 - 4x
y = (15 - 4x)/6
3x - 4y = 7
4y = 3x - 7
y = (3x - 7)/4
Find x:
4(15 - 4x) = 6(3x - 7)
2(15 - 4x) = 3(3x - 7)
30 - 8x = 9x - 21
17x = 51
x = 3
Find y:
= (15 - 4[3])/6
= (15 - 12)/6
= 3/6 or 1/2
Answer: x = 3, y = 1/2
Proof:
(4[3] + 6[1/2]) - (3[3] - 4[1/2]) = 15 - 7
(12 + 3) - (9 - 2) = 8
15 - (7) = 8
15 - 7 = 8
8 = 8
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21
adjr221's avatar
adjr221
1 decade ago
3x-4y=7 ====> (3x-7)/4=y
subsit. y in the second equation you get
4x+6(3x-7)/4=15 now solve for x ===> x=3
replace the x in the first equation 3x-4y=7 and solve for y
3(3)-4y=7 ===> y=1/2
the answer on the top are not correct. try placing the values of x and y in the equations and see for your self
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11
♪£yricảl♪'s avatar
♪£yricảl♪
Lv 4
1 decade ago
4x+6y=15 ---[1]
3x-4y=7 ---[2]
From [1],
4x = 15 - 6y
x = (15 - 6y) / 4 ---[3]
Sub. [3] into [2],
3[(15 - 6y) / 4] - 4y = 7
(45 - 18y) / 4 - 4y = 7
(45 - 18y) - 16y = 28
45 - 34y = 28
34y = 17
y = 1/2
Sub. (y = 1/2) into [3],
=> x = (15 - 6y) / 4
=> x = [15 - 6(1/2)] / 4
=> x = [15 - 3] / 4
=> x = 3
x = 3
y = 1/2
The solution is x = 3 and y = 1/2
Given: The equations 4x + 6y = 15 and 3x - 4y = 7.
To Find: The value of x and y using the substitution method.
Solution:
- The substitution method is done by taking a variable in terms of another from one equation and putting the value in the respective position of the second equation.
Coming to the numerical, we are given 2 equations,
4x + 6y = 15 ...(1)
3x - 4y = 7 ...(2)
We can write equation (2) like this,
3x = 7 + 4y
⇒ x = ( 4y + 7 )/3 ... (3)
Now, we shall put (3) in equation (1) and solve for 'y',
4x + 6y = 15
⇒ 4 × ( 4y + 7 )/3 + 6y = 15
⇒ 16y/3 + 28/3 + 6y = 15
⇒ 34y/3 = 17/3
⇒ y = ( 17/3 ) / ( 3/34 )
⇒ y = 1/2 ....(4)
Putting (4) in (2), we get
3x - 4y = 7
⇒ 3x - 4 × 1/2 = 7
⇒ 3x = 9
⇒ x = 3
Hence, the solution is x = 3 and y = 1/2.
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