Lisa invests $4,000 in two types of bonds, bond a and bond b. bond a offers a 10% return, and bond b offers a 6% return. lisa invests $x in bond a and $y in bond b. her total return on the investment is $340.
the system of linear equations defining the situation is . the amount lisa invested at the rate of 10% is , and the amount she invested at the rate of 6% is .

The amount invested at the rate of 10% is $2500 and that of 6% is $1500.

Step-by-step explanation:  Given that Lisa invests $4,000 in two types of bonds, bond A and bond B. Bond A offers a 10% return, and bond B offers a 6% return.

Lisa invests $x in bond A and $y in bond B and her total return on the investment is $340.

According to the given information, the system of linear equations can be written as

Multiplying equation (i) by 5, we have

Subtracting equation (ii) from equation (iii), we get

and from equation (i), we get

Thus, the system of linear equations defining the situation is

and

the amount Lisa invested at the rate of 10% is $2500 and the amount she invested at the rate of 6% is $1500.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47