Solve the system x+y-14=0 4x-y-11=0
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We have to solve:
x + y - 14 = 0 ...(1)
4x - y - 11 = 0 ...(2)
From (1)
x + y - 14 = 0
=> -y = x - 14
Substitute in (2)
4x + x - 14 - 11 = 0
=> 5x - 25 = 0
=> x = 25/5
=> x = 5
y = 14 - x
=> y = 14 - 5
=> y = 9
The required solution is x = 5 and y = 9
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x+y-14=0
x = 14 - y
replace y
4x-y-11=0
subtract 11
4(14 - y) - y = 11
56 - 4y - y = 11
combine like terms
- 4y - y = -56 + 11
-5y = -45
divide by -5
y = 9
now plug this in as y to get x
x+9-14=0
x - 5=0
add 5
x= 5
x+y-14=0
x = 14 - y
now replace y with those numbers in any of the equations:
4x-y-11=0
subtract 11
4(14 - y) - y = 11
56 - 4y - y = 11
combine like therms
- 4y - y = -56 + 11
-5y = -45
divide by -5
- y = 9
now plug this in as y to get x
x+9-14=0
x - 5=0
add 5
- x= 5
We'll re-write the equations, keeping the variables x and y to the left side:
x + y = 14 (1)
4x - y = 11 (2)
We'll solve the system using substitution:
x = 14 - y (3)
We'll replace x in the 2nd equation by the expression from (3):
4(14 - y) - y = 11
We'll remove the brackets:
56 - 4y - y = 11
-5y = 11 - 56
-5y = -45
We'll divide by -5:
y = 9
We'll substitute y in (3):
x = 14 - 9
x = 5
The solution of the system is the pair: (5 ; 9).
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