5x-2y=13 and 10x-8y=26 are the pair of linear equation is
Answers
Answer:
Answer:
5x-2y=9____(1)×4
3x+4y=4___(2)×2
20x-8y=36
6x+8y=8
______
26x=44
x=22/13
from equation (1)
5x-2y=9
5×22/13-2y=9
110/13-2y=9
-9+110/13=2y
7/13=2y
y=7/26
Step-by-step explanation:
Answer:
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Step-by-step explanation:
Here are some more examples of using substitution to solve simultaneous equations:
3x + y = 13
5x -2y = 7
The coefficient of y in Equation 1 is 1. So first we make y the subject of Equation 1:
y = 13 - 3x
Next, substitute this expression for y in Equation 2 and solve for x:
5x - 2(13 - 3x) = 7 Multiply out bracket
5x - 26 + 6x = 7 Combine like terms (x's on one side, numbers on the other)
11x = 33 Divide both sides by 11 to solve for x
x = 3
Finally, substitute the solution for x into the expression for y:
y = 13 - 3(3) = 4
y = 4
So the solution to the pair of simultaenous linear equations is (3,4).
2x + 4y = 10
2x + y = 4
The coefficient of y in Equation 2 is 1. So first we make y the subject of Equation 2:
y = 4 - 2x
Next, substitute this expression for y in Equation 1 and solve for x:
2x + 4(4 - 2x) = 10 Multiply out bracket
2x + 16 - 8x = 10 Combine like terms (x's on one side, numbers on the other)
-6x = -6 Divide both sides by -6 to solve for x
x = 1
Finally, substitute the solution for x into the expression for y:
y = 4 - 2(1) = 2
y = 2
So the solution to the pair of simultaenous linear equations is (1,2).
x - 5y = 7
2x -4y = 8
The coefficient of x in Equation 1 is 1. So first we make x the subject of Equation 1:
x = 7 + 5y
Next, substitute this expression for x in Equation 2 and solve for y:
2(7 + 5y) - 4y = 8 Multiply out bracket
14 + 10y - 4y = 8 Combine like terms (y's on one side, numbers on the other)
6y = -6 Divide both sides by 6 to solve for y
y = -1
Finally, substitute the solution for y into the expression for x:
x = 7 + 5(-1) = 2
x = 2
So the solution to the pair of simultaenous linear equations is (2,-1).
2x + 4y = 12
x + 8y = 30
The coefficient of x in Equation 2 is 1. So first we make x the subject of Equation 2:
x = 30 - 8y
Next, substitute this expression for x in Equation 1 and solve for y:
2(30 - 8y) + 4y = 12 Multiply out bracket
60 - 16y + 4y = 12 Combine like terms (y's on one side, numbers on the other)
-12y = -48 Divide both sides by -12 to solve for y
y = 4
Finally, substitute the solution for y into the expression for x:
x = 30 - 8(4) = -2
x = -2
So the solution to the pair of simultaenous linear equations is (-2,2).
2x - 4y = 10
-4x+5y = -26
None of the coefficients are 1. So we can choose to make any variable the subject.
Lets make x the subject of Equation 1:
x = (10 + 4y)/2
x = 5 + 2y
Next, substitute this expression for x in Equation 2 and solve for y:
-4(5 + 2y ) + 5y = -26
-20 - 8y + 5y = -26
-3y = -6
y = 2
Finally, substitute the solution for y into the expression for x:
x = 5 + 2(2) = 9
x = 9
So the solution to the pair of simultaenous linear equations is (9,2).
6x + 2y = 10
10x - 3y = 12
None of the coefficients are 1. So we can choose to make any variable the subject.
Lets make y the subject of Equation 2:
y = (12-10x)/(-3)
y = -4 + (10/3) x
Next, substitute this expression for y in Equation 1 and solve for x:
6x + 2(-4 + (10/3) x) = 10
6x - 8 + (20/3) x = 10
(38/3) x = 18
x = 18*(3/38) = 27/19
Finally, substitute the solution for x into the expression for y:
y = -4 + (10/3)/(27/19) = -4 + 270/57 = -228/57 = 270/57 = 42/57 = 14/19
So the solution to the pair of simultaenous linear equations is (27/19,5/19).
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