a total of $ 14,000 is invested in two funds paying 4% and 5% annual interest. The combined interest is $620 a)write a system of equations to model this problem b). graph this system and use the graph to estimate how much was invested in each fund?

how about

x+y = 14000
.04x + .05y = 620 --- 4x + 5y = 62000

graph using intercepts,
for x+y = 1400 ---> (0,14000) (14000,0)
for 4x+5y=62000 --->(0,12400), (15500,0)

on your grid, let each unit be 1000

To solve this problem, we can set up a system of equations based on the information given.

Let's assume that the amount invested in the fund paying 4% is represented by 'x' dollars, and the amount invested in the fund paying 5% is represented by 'y' dollars.

a) Writing the equations:
1. The first equation represents the total amount invested:
x + y = 14,000 (Equation 1)

2. The second equation represents the combined interest earned:
0.04x + 0.05y = 620 (Equation 2)

b) Graphing the system of equations:
To graph the system, we need to convert the equations into slope-intercept form (y = mx + b).

Equation 1: x + y = 14,000
Rearranging, we get: y = -x + 14,000

Equation 2: 0.04x + 0.05y = 620
Multiplying by 100 to remove decimals, we get: 4x + 5y = 62,000
Rearranging, we get: y = (-4/5)x + 12,400

Now, we can graph these two equations on the same coordinate plane.

The graph will have two intersecting lines representing the solutions to the system. The point of intersection will provide an estimate of the amount invested in each fund.

To estimate the values graphically, we find the point of intersection on the graph and read the x and y-values. These values will represent the approximate amounts invested in each fund.

Note: The graph may not give an exact value due to the limitations of reading values from a graph. To obtain an exact solution, we can solve the system of equations algebraically using methods such as substitution, elimination, or matrix methods.