To solve the system of equations by addition, we want to eliminate one variable by adding the equations together. Let's start by multiplying the first equation by -0.02 to make the coefficients of y in both equations the same.
-0.02(x) + (-0.02)(y) = (-0.02)(y + 600)
-0.02x - 0.02y = -0.02y - 12
Now we can add the two equations together:
0.08x + 0.02y + (-0.02x) + (-0.02y) = 470 + (-12)
0.06x = 458
Divide both sides of the equation by 0.06:
x = 458 / 0.06
x = 7633.33
Now we can substitute this value of x back into the first equation to solve for y:
y = x - 600
y = 7633.33 - 600
y = 7033.33
Therefore, the amount invested at the rate of 8% is $7633.33, and the amount invested at the rate of 2% is $7033.33.
Solve the following word problem.
Money is invested at two rates of interest. One rate is 8%
and the other is 2%
. If there is $600
more invested at 8%
than at 2%
, find the amount invested at each rate if the total annual interest received is $470
. Let x=
amount invested at 8%
and y=
amount invested at 2%
. Then the system that models the problem is {x=y+600 0.08x+0.02y=470
. Solve the system by using the method of addition.
1 answer
1 answer