3x -5y - 4 =0 and 9x=2y+7 solve the following pair of linear equations by the elimination method and the substitution method.
Answers
Step-by-step explanation:
3x-5y=4.........[1]
9x-2y=7..........[2]
multiply by 3 equation [1]
9x-15y=12 .........[3]
subtracting from equation [1] and [3]
9x-15y = 12
- 9x+2y= -7
X= -13/5
this values put the equation [1]
3×[-13/5]-5y=4
-39/5 -5y = 4
-5y = 4+39/5
-5y = 20+39 / 5
-5y = 59/5
y= 59/25
Answer: 3x – 5y – 4 = 0 and 9x = 2y + 7
By elimination method
3x – 5y – 4 = 0
3x – 5y = 4 ...(i)
9x = 2y + 7
9x – 2y = 7 ... (ii)
Multiplying equation (i) by 3, we get
9 x – 15 y = 11 ... (iii)
9x – 2y = 7 ... (ii)
Subtracting equation (ii) from equation (iii), we get
-13y = 5
y = -5/13
Putting value in equation (i), we get
3x – 5y = 4 ... (i)
3x - 5(-5/13) = 4
Multiplying by 13 we get
39x + 25 = 52
39x = 27
x =27/39 = 9/13
Hence our answer is x = 9/13 and y = - 5/13
By substitution method
3x – 5y = 4 ... (i)
Adding 5y both side we get
3x = 4 + 5y
Dividing by 3 we get
x = (4 + 5y )/3 ... (iv)
Putting this value in equation (ii) we get
9x – 2y = 7 ... (ii)
9 ((4 + 5y )/3) – 2y = 7
Solve it we get
3(4 + 5y ) – 2y = 7
12 + 15y – 2y = 7
13y = - 5
y = -5/13
x = 4 + 5 ( -5/13)/ 3
= 4 - 25/13 / 3
= 4 × 13 - 25/13 / 3
= 27/13×3
= 27/39
= 9/13
Hence we get x = 9/13 and y = - 5/13 again.
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