Find the values of x and y if x + 2y = 4 and 2x - 3y = 5.
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We have to find the solution of :
x + 2y = 4 ...(1)
2x - 3y = 5 ...(2)
2*(1) - (2)
=> 2x + 4y - 2x + 3y = 8 - 5
=> 7y = 3
=> y = 3/7
substitute in (1)
x = 4 - 3*2/7
=> 4 - 6/7
=> 22/7
The solution of the system of equations is x = 22/7 and y = 3/7
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x + 2y = 4 and 2x - 3y = 5
x = 4 - 2y
2(4 - 2y) - 3y = 5
8 - 4y - 3y = 5
8 - 7y = 5
-7y = 5 - 8
-7y = -3
y = -3/-7
y =3.14
x + 2(3/7) = 4
2(3/7) =0.86
x + .86 = 4
subtract .86
x = 4 - .86
y = 3.14
x + 2y = 4 and 2x - 3y = 5
you can do this many ways one of those will be by subtracting 2y from x + 2y = 4
x = 4 - 2y
now plug in this number as x in the other problem:
2(4 - 2y) - 3y = 5
distribute the 2:
8 - 4y - 3y = 5
combine like terms
8 - 7y = 5
subtract the 8:
-7y = 5 - 8
-7y = -3
divide by -7
y = -3/-7
the negatives cancel each other out:
y = 3/7 or .43
to find x just plug in 3/7 as y in any of the equations above:
x + 2(3/7) = 4
2(3/7) = 0.857142857 or 0.86
simplify:
x + .86 = 4
subtract .86
x = 4 - .86
x = 3.14
Given the equations.
x+2y = 4..(1)
x-3y = 5..(2), we are required to solve for x and y.
We compute (1) - (2):
x+2y- (x-3y) = 4-5
x+2y-x+3y = 4-5 = -1
x's cancels and we get
2y+3y = -1
5y = -1
y= -1/5.
Put y = -1/5 in (2): x -3y = 5
x - 3(-1/5) = 5
x+3/5 = 5
x = 5-3/5 = 22/5.
x = 22/5 , y = -1/5.
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