Answer:
[tex]\begin{gathered} A_1=x=\operatorname{\$}3,100 \\ \\ A_2=y=\operatorname{\$}3,200 \end{gathered}[/tex]Explanation: Scott Invested in two banks, and each bank paid 9% and 10% yearly interest. the total amount invested was $6300 and the Interest earned in the first year is $598. We have to find the amount invested in each bank.
Mathematical Formula:
let us say that amount x was invested in the first bank and amount y was invested in the second bank, considering this we can write the following equation for the total money invested:
[tex]\begin{gathered} x+y=\$6300\Rightarrow(1) \\ \end{gathered}[/tex]Similarly, the following is the equation for the total Interest earned in the first year.
[tex](0.1)x+(0.09)y=\$598\Rightarrow(2)[/tex]Equation (1) and (2) are two linear simultaneous equations:
[tex]\begin{cases}x+y={6300} \\ (0.1)x+(0.09)y={598}\end{cases}[/tex]The graphical solution to the above system is as follows:
Therefore the amount invested in each bank is:
[tex]\begin{gathered} x=\$3,100 \\ y=\$3,200 \\ \\ \because\rightarrow \\ x+y=\$3,100+3,200=\$6,300\rightarrow\text{ \lparen Checks out\rparen} \end{gathered}[/tex]Scott invested $3,100 in the first bank and in the second bank, he invested $3,200.
