if 4x +3y = 9 and 3x + 4y = - 8, then x - y =
Answers
x-y = 17
Step-by-step explanation:
We are given two equations: 4x+3y = 9 and 3x+4y = -8. Let us solve these equations by elimination method.
⟹ 4x+3y = 9 ---(1)
⟹ 3x+4y = -8 ---(2)
On multiplying (3) and (4) in Equation 1 and Equation 2, we get:
⟹ 3(4x+3y) = 3(9)
⟹ 12x+9y = 27 ---(3)
Similarly,
⟹ 4(3x+4y) = 4(-8)
⟹ 12x+16y = -32 ---(4)
On subtracting Equation(3) from Equation(4), we get:
⟹ 12x+16y-(12x+9y) = -32-27
⟹ 12x+16y-12x-9y = -59
⟹ 16y-9y = -59
⟹ 7y = -59
⟹ y = -59/7
Let us substitute the value of y in any equation, let's say (1):
⟹ 4x+3y = 9
⟹ 4x+3(-59/7) = 9
⟹ 4x-177/7 = 9
⟹ 4x = 9+177/7
On taking LCM, we get:
⟹ 4x = (63+177)/7
⟹ 4x = 240/7
⟹ x = 240/(7×4)
⟹ x = 240/28
⟹ x = 60/7
Hence,
⟹ x = 60/7
⟹ y = -59/7
Now, according to the question, we need to find the value of x-y.
⟹ x-y = 60/7-(-59/7)
⟹ x-y = 60/7+59/7
⟹ x-y = 119/7
⟹ x-y = 17
Hence, the value of x-y is 17.
Answer:
4x+3y=9. --------(i)
3x+4y=-8 ---------(ii)
by subtracting we get,
x-y=17