To solve the system of equations by the method of addition, we can add the two equations together to eliminate one variable.
x = y + 1400
0.07x + 0.02y = 440
First, we can multiply the second equation by 100 to get rid of the decimal points:
100(0.07x + 0.02y) = 100(440)
7x + 2y = 44000
Now we can add the two equations together:
(x) + (7x + 2y) = (y + 1400) + (44000)
8x + 2y = y + 45400
Next, we can simplify the equation by combining like terms:
8x + 2y - y = 45400
8x + y = 45400
Now we have eliminated one variable and can solve for x.
To do this, we can subtract y from both sides of the equation:
8x = 45400 - y
Now we can substitute the expression for x from the first equation into the second equation:
x = (45400 - y) / 8
Substituting this expression for x into the first equation gives:
(45400 - y) / 8 = y + 1400
Next, we can multiply both sides of the equation by 8 to clear the fraction:
45400 - y = 8(y + 1400)
Expanding the equation gives:
45400 - y = 8y + 11200
Now we can combine like terms:
45400 - 11200 = 8y + y
34200 = 9y
Next, we can divide both sides of the equation by 9 to solve for y:
y = 34200 / 9
y = 3800
Now, substituting this value of y back into the expression for x:
x = y + 1400
x = 3800 + 1400
x = 5200
Therefore, the amount invested at 7% is $5200, and the amount invested at 2% is $3800.