You have a total of ​$1760 to invest. Account A pays 7​% annual interest and account B pays 4​% annual interest. How much should you invest in each account if you would like the investment to earn ​$ 95 at the end of one​ year? Let A represent the amount of money invested in the account that earns 7​% annual interest and let B represent the amount of money invested in the account that earns 4​% annual interest. Complete the system of linear equations to solve the problem.

Answer:You should invest $820 in account A and $940 in account BStep-by-step explanation:* Lets use the system of linear equations to solve the problem- Simple Interest Equation I = Prt , Where:# P = Invested Amount# I = Interest Amount# r = Rate of Interest per year in decimal; r = R/100# t = Time Period involved in months or years* Lets solve the problem- The total money invested is $1760- Account A pays 7​% annual interest- Account B pays 4​% annual interest- Let A represent the amount of money invested in the account A- Let B represent the amount of money invested in the account B- You would like to earn $ 95 at the end of one year∴ The interest from both accounts at the end of one year is $95- Lets write the equations# Account A :∵ Account A has $A invested∴ P = $A∵ Account A pays 7​% annual interest ∴ r = 7/100 = 0.07∵ t = 1 year∵ I = Prt∴ I = A(0.07)(1) = 0.07A# Account B :∵ Account B has $B invested∴ P = $B∵ Account A pays 4​% annual interest ∴ r = 4/100 = 0.04∵ t = 1 year∵ I = Prt∴ I = B(0.04)(1) = 0.04B- The total amount of interest from both accounts at the end of one   year is $95∴ I from A + I from B = 95∴ 0.07A + 0.04B = 95 ⇒ multiply both sides by 100∴ 7A + 4B = 9500 ⇒ (1)- The total money to invest in both accounts is $1760∵ Account A has $A invested∵ Account B has $B invested∴ A + B = 1760 ⇒ (2)* Lets solve the system of equations to find the amount of money   invested in each account- Multiply equation (2) by -4 to eliminate B∵ A + B = 1760 ⇒ × -4∴ -4A - 4B = -7040 ⇒ (3)- Add equation (1) and (3)∵ 7A + 4B = 9500 ⇒ (1)∵ -4A - 4B = -7040 ⇒ (3)∴ 7A - 4A = 9500 - 7040∴ 3A = 2460 ⇒ divide both side by 3∴ A = 820- Substitute the value of A in equation (1) or (2)∵ A + B = 1760 ⇒ (2)∴ 820 + B = 1760 ⇒ subtract 820 from both sides∴ B = 940- From all above* You should invest $820 in account A and $940 in account B