Question

Two investments totaling 56,500 produce an annual income of $1835. One investment yields 4 % per year while the other yields 3 % per year how much is invested at each rate

Answer 1

FIRST EQUATION (we know that the two investments add up to $56,500)
X + Y = 56,500

SECOND EQUATION (we know that one investment makes 4% and one makes 3% and the total adds up to $1835)
.04X + .03Y = 1,835

Now simplify the second equation. First, multiply both sides by 25 so that we have 1X, just like in the first equation.
25(.04X + .03Y) = 25 * 1,835
X + .75Y = 45,875

Next, multiply both sides by -1 so that the 1X becomes -1X, which will allow us to subtract the X from the first equation and only have to deal with one variable, the Y.

-1(x + .75Y) = -1*45,875
-X -.75Y = -45,875

Now take the first equation and subtract the second equation from it:
X + Y = 56,500
-X -.75Y = -45,875
.25Y = 10625

Solve for Y by dividing both sides by .25.
Y = 42500

Solve for X by plugging the value of Y into the first equation.
X = 14100

Hope this helps !