Question 1186847
x equals the first investment.
y = the second investment.


your two equations that need to be solved simultaneously are:


.08 * x + .02 * y = 780
.10 * x + .01 * y = 810


multiply both sides of the second equation by 2 and leave the first equation as is to get:


.08 * x + .02 * y = 780
.20 * x + .02 * y = 1620


subtract the first equation from the second to get:


.12 * x = 840


solve for x to get:

x = 840 / .12 = 7000


in the first original equation, replace x with 7000 to get:


.08 * x + .02 * y = 780 becomes:


.08 * 7000 + .02 * y = 780


simplify to get:


560 + .02 * y = 780


subtract 560 from both sides of the equation to get:


.02 * y = 220


solve for y to get:


y = 220 / .02 = 11000


you have:


x = 7000 and y = 11000.


that's  your answer.


confirm by replacing x with 7000 and y with 1100 in the original two equations.


you get:


.08 * x + .02 * y = 780 becomes .08 * 7000 + 02 * 11000 = 780 which becomes 560 + 220 = 780 which becomes 780 = 780, confirming the value of x and y in the first equation is good.


.10 * x + .01 * y = 810 becomes .10 * 7000 + .01 * 11000 = 810 which becomes 700 + 110 = 810 which becomes 810 = 810, confirming the value of x and y in the second equation is good.


your solution of x = 7000 and y = 11000 is confirmed to be good.


that's how much she invested in each fund.